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In this paper, a link between a time-consistent and a pre-commitment investment strategy is established. We define an implied investment target, which is implicitly con- tained in a time-consistent strategy at a given time step and wealth level. By imposing the implied investment target at the initial time step on a time-consistent strategy, we form a hybrid strategy which may generate better mean-variance efficient frontiers than the time-consistent strategy. We extend the numerical algorithm proposed in Cong and Oosterlee (2016b) to solve constrained time-consistent mean-variance optimization pro- blems. Since the time-consistent and the pre-commitment strategies generate different terminal wealth distributions, time-consistency is not always inferior to pre-commitment.

BackgroundIn the absence of horizontal gene transfer it is possible to reconstruct the history of gene families from empirically determined orthology relations, which are equivalent toevent-labeledgene trees. Knowledge of the event labels considerably simplifies the problem of reconciling a gene treeTwith a species treesS, relative to the reconciliation problem without prior knowledge of the event types. It is well-known that optimal reconciliations in the unlabeled case may violate time-consistency and thus are not biologically feasible. Here we investigate the mathematical structure of the event labeled reconciliation problem with horizontal transfer.ResultsWe investigate the issue of time-consistency for the event-labeled version of the reconciliation problem, provide a convenient axiomatic framework, and derive a complete characterization of time-consistent reconciliations. This characterization depends on certain weak conditions on the event-labeled gene trees that reflect conditions under which evolutionary events are observable at least in principle. We give an 𝒪(|V(T)|log(|V(S)|))-time algorithm to decide whether a time-consistent reconciliation map exists. It does not require the construction of explicit timing maps, but relies entirely on the comparably easy task of checking whether a small auxiliary graph is acyclic. The algorithms are implemented in C++ using the boost graph library and are freely available athttps://github.com/Nojgaard/tc-recon.SignificanceThe combinatorial characterization of time consistency and thus biologically feasible reconciliation is an important step towards the inference of gene family histories with horizontal transfer from orthology data, i.e., without presupposed gene and species trees. The fast algorithm to decide time consistency is useful in a broader context because it constitutes an attractive component for all tools that address tree reconciliation problems.

In this paper, we propose the notion of dynamic deviation measure, as a dynamic time-consistent extension of the (static) notion of deviation measure. To achieve time-consistency, we require that a dynamic deviation measures satisfies a generalised conditional variance formula. We show that, under a domination condition, dynamic deviation measures are characterised as the solutions to a certain class of stochastic differential equations. We establish for any dynamic deviation measure an integral representation, and derive a dual characterisation result in terms of additively $m$-stable dual sets. Using this notion of dynamic deviation measure, we formulate a dynamic mean-deviation portfolio optimization problem in a jump-diffusion setting and identify a subgame-perfect Nash equilibrium strategy that is linear as function of wealth by deriving and solving an associated extended HJB equation.

In this paper I propose a time-consistent method of discounting hyperbolically and apply it to three canonical environmental problems: (i) optimal renewable resource use, (ii) the tragedy of the commons, (iii) economic growth and pollution. I then compare results with those for conventional exponential discounting using the normalization that both methods provide the same present value of an infinite constant flow. I show that, irrespective of potentially high initial discount rates, time-consistent hyperbolic discounting leads always to a steady state of maximum yield, or, if the environment enters the utility function, a steady state where the Green Golden Rule applies. While (asymptotic) extinction is a real threat under exponential discounting it is impossible under time-consistent hyperbolic discounting. This result is also confirmed for open access resources. In a model of economic growth and pollution, hyperbolic discounting establishes the Golden Rule of capital accumulation and the Modified Green Golden Rule. October 2017

We study optimal time-consistent distortionary taxation when the repayment of government debt is not enforceable. The government taxes labor income or issues noncontingent debt in order to finance an exogenous stream of stochastic government expenditures. The government can repudiate its debt subject to some default costs, thereby introducing some state-contingency to debt. We are motivated by the fact that domestic sovereign default is an empirically relevant phenomenon, as Reinhart and Rogoff (2011) demonstrated. Optimal policy is characterized by two opposing incentives: an incentive to postpone taxes by issuing more debt for the future and an incentive to tax more currently in order to avoid punishing default premia. A generalized Euler equation (GEE) captures these two effects and determines the optimal back-loading or front-loading of tax distortions.

We consider evaluation methods for payoffs with an inherent financial risk as encountered for instance for portfolios held by pension funds and insurance companies. Pricing such payoffs in a way consistent to market prices typically involves combining actuarial techniques with methods from mathematical finance. We propose to extend standard actuarial principles by a new market-consistent evaluation procedure which we call "two-step market evaluation." This procedure preserves the structure of standard evaluation techniques and has many other appealing properties. We give a complete axiomatic characterization for two-step market evaluations. We show further that in a dynamic setting with continuous stock prices every evaluation which is time-consistent and market-consistent is a two-step market evaluation. We also give characterization results and examples in terms of g-expectations in a Brownian-Poisson setting.

This chapter provides an in-depth overview of an extended set of multi-period risk measures, their mathematical and economic properties, primarily from the perspective of dynamic risk control and portfolio optimization. The analysis is structured in four parts: the first part reviews characterizing properties of multi-period risk measures, it examines their financial foundations, and clarifies cross-relationships. The second part is devoted to three classes of multi-period risk measures, namely: terminal, additive and recursive. Their financial and mathematical properties are considered, leading to the proposal of a unifying representation. Key to the discussion is the treatment of dynamic risk measures taking their relationship with evolving information flows and time evolution into account: after convexity and coherence, time consistency emerges as a key property required by risk measures to effectively control risk exposure within dynamic programs. In the third part, we consider the application of multi-period measures to optimal investment policy selection, clarifying how portfolio selection models adapt to different risk measurement paradigms. In the fourth part we summarize and point out desirable developments and future research directions. Throughout the chapter, attention is paid to the state-of-the-art and methodological and modeling implications.

Recursive utility disentangles preferences with respect to time and risk by recursively building up a value function of local increments. This involves certainty equivalents of indirect utility. Instead we disentangle preferences with respect to time and risk by building up a value function as a non-linear aggregation of certainty equivalents of direct utility of consumption. This entails time-consistency issues which are dealt with by looking for an equilibrium control and an equilibrium value function rather than a classical optimal control and a classical optimal value function. We characterize the solution in a general diffusive incomplete market model and find that, in certain special cases of utmost interest, the characterization coincides with what would arise from a recursive utility approach. But also importantly, in other cases, it does not: The two approaches are fundamentally different but match, exclusively but importantly, in the mathematically special case of homogeneity of the value function.

Mean-variance criteria remain prevalent in multi-period problems, and yet not much is known about their dynamically optimal policies. We provide a fully analytical characterization of the optimal dynamic mean-variance portfolios within a general incomplete-market economy, and recover a simple structure that also inherits several conventional properties of static models. We also identify a probability measure that incorporates intertemporal hedging demands and facilitates much tractability in the explicit computation of portfolios. We solve the problem by explicitly recognizing the time-inconsistency of the mean-variance criterion and deriving a recursive representation for it, which makes dynamic programming applicable. We further show that our time-consistent solution is generically different from the pre-commitment solutions in the extant literature, which maximize the mean-variance criterion at an initial date and which the investor commits to follow despite incentives to deviate. We illustrate the usefulness of our analysis by explicitly computing dynamic mean-variance portfolios under various stochastic investment opportunities in a straightforward way, which does not involve solving a Hamilton-Jacobi-Bellman differential equation. A calibration exercise shows that the mean-variance hedging demands may comprise a significant fraction of the investor's total risky asset demand.

International audience; In stochastic optimal control, one deals with sequential decision-making under uncertainty; with dynamic risk measures, one assesses stochastic processes (costs) as time goes on and information accumulates. Under the same vocable of time-consistency (or dynamic-consistency), both theories coin two different notions: the latter is consistency between successive evaluations of a stochas-tic processes by a dynamic risk measure (a form of monotonicity); the former is consistency between solutions to intertemporal stochastic optimization problems. Interestingly, both notions meet in their use of dynamic programming, or nested, equations. We provide a theoretical framework that offers i) basic ingredients to jointly define dynamic risk measures and corresponding intertemporal stochastic optimization problems ii) common sets of assumptions that lead to time-consistency for both. We highlight the role of time and risk preferences — materialized in one-step aggregators — in time-consistency. Depending on how one moves from one-step time and risk preferences to intertemporal time and risk preferences, and depending on their compatibility (commutation), one will or will not observe time-consistency. We also shed light on the relevance of information structure by giving an explicit role to a state control dynamical system, with a state that parameterizes risk measures and is the input to optimal policies.

We analyze the Foster–Hart measure of riskiness for general distributions in dynamic settings. The Foster–Hart measure avoids bankruptcy in the long run. It is not time-consistent.

This paper studies the optimal management of the maturity of government debt in an economy without commitment. We consider a reputation where any deviation triggers reversion to the worst sustainable equilibrium. We obtain two results. First, contrary to earlier literature, we show that a very rich debt structure is not a necessary condition to solve the time-inconsistency problem. Second, we learn how to allocate the outstanding debt into short and long-term bonds to enhance the credibility of the government policy. (Copyright: Elsevier)

This article develops a multi-period production model to examine the optimal dynamic behaviour of a large monopolistic value-maximizing firm that manipulates its valuation as well as the price of its output. In the pre-commitment equilibrium the firm’s output and labour demand are decreased, while the price of consumption is increased, as compared with its competitive counterpart. Profits and the firm's value can, however, be either increased or decreased. In the time-consistent equilibrium the firm’s output and labour demand are increased, while the price of consumption is decreased. More strikingly, the profits in every period are decreased, and may even go negative, while the firm's value can be either lower or higher than in the competitive benchmark. In the continuous-time limit, while the pre-commitment equilibrium retains its basic discrete-time structure, the time-consistent equilibrium tends to the limit of zero profits and hence zero firm's value.

Stochastic optimal control addresses sequential decision-making under uncertainty. As applications leads to large-size optimization problems, we count on decomposition methods to tackle their mathematical analysis and their numerical resolution. We distinguish two forms of decomposition. In chained decomposition, like Dynamic Programming, the original problemis solved by means of successive smaller subproblems, solved one after theother. In parallel decomposition, like Progressive Hedging, the original problemis solved by means of parallel smaller subproblems, coordinated and updated by amaster algorithm. In the first part of this manuscript, Dynamic Programming: Risk and Convexity, we focus on chained decomposition; we address the well known time decomposition that constitutes Dynamic Programming with two questions. In Chapter 2, we extend the traditional additive in time and risk neutral setting to more general ones for which we establish time-consistency. In Chapter 3, we prove a convergence result for the Stochastic Dual Dynamic Programming Algorithm in the case where (convex) cost functions are no longer polyhedral. Then, we turn to parallel decomposition, especially decomposition methods obtained by dualizing constraints (spatial or non-anticipative). In the second part of this manuscript, Duality in Stochastic Optimization, we first point out that such constraints lead to delicate duality issues (Chapter 4).We establish a duality result in the pairing Bp{L∞,L¹} in Chapter 5. Finally, in Chapter 6, we prove the convergence of the Uzawa Algorithm in L∞(Ω,F,ℙ;ℝ^n). The third part of this manuscript, Stochastic Spatial Decomposition Methods, is devoted to the so-called Dual Approximate Dynamic Programming Algorithm. In Chapter 7, we prove that a sequence of relaxed optimization problems epiconverges to the original one, where almost sure constraints are replaced by weaker conditional expectation ones and that corresponding σ-fields converge. In Chapter 8, we give theoretical foundations and interpretations to the Dual Approximate Dynamic Programming Algorithm, Le contrôle optimal stochastique (en temps discret) s'intéresse aux problèmes de décisions séquentielles sous incertitude. Les applications conduisent à des problèmes d'optimisation degrande taille. En réduisant leur taille, les méthodes de décomposition permettent le calcul numérique des solutions. Nous distinguons ici deux formes de décomposition. La emph{décomposition chaînée}, comme la Programmation Dynamique, résout successivement, des sous-problèmes de petite taille. La décomposition parallèle, comme le Progressive Hedging, consiste à résoudre itérativement et parallèlement les sous-problèmes, coordonnés par un algorithme maître. Dans la première partie de ce manuscrit, Dynamic Programming: Risk and Convexity, nous nous intéressons à la décomposition chaînée, en particulier temporelle, connue sous le nom de Programmation Dynamique. Dans le chapitre 2, nous étendons le cas traditionnel, risque-neutre, de la somme en temps des coûts, à un cadre plus général pour lequel nous établissons des résultats de cohérence temporelle. Dans le chapitre 3, nous étendons le résultat de convergence de l'algorithme SDDP (Stochastic Dual Dynamic Programming Algorithm) au cas où les fonctions de coûts (convexes) ne sont plus polyhédrales. Puis, nous nous tournons vers la décomposition parallèle, en particulier autour des méthodes de décomposition obtenues en dualisant les contraintes (contraintes spatiales presque sûres, ou de non-anticipativité). Dans la seconde partie de ce manuscrit, Duality in Stochastic Optimization, nous commençons par souligner que de telles contraintes peuvent soulever des problèmes de dualité délicats (chapitre 4). Nous établissons un résultat de dualité dans les espaces pairés Bp{L∞,L¹} au chapitre 5. Finalement, au chapitre 6, nous montrons un résultat de convergence de l'algorithme d'Uzawa dans L∞(Ω,F,ℙ;ℝ^n), qui requière l'existence d'un multiplicateur optimal. La troisième partie de ce manuscrit, Stochastic Spatial Decomposition Methods, est consacrée à l'algorithme connu sous le nom de DADP (Dual Approximate Dynamic Programming Algorithm). Au chapitre 7, nous montrons qu'une suite de problèmes d'optimisation où une contrainte presque sûre est relaxée en une contrainte en espérance conditionnelle épi-converge vers le problème original si la suite des tribus converge vers la tribu globale. Finalement, au chapitre 8, nous présentons l'algorithme DADP, des interprétations, et des résultats de convergence basés sur la seconde partie du manuscrit

We consider evaluation methods for payoffs with an inherent financial risk as encountered for instance for portfolios held by pension funds and insurance companies. Pricing such payoffs in a way consistent to market prices typically involves combining actuarial techniques with methods from mathematical finance. We propose to extend standard actuarial principles by a new market-consistent evaluation procedure which we call ‘two step market evaluation.’ This procedure preserves the structure of standard evaluation techniques and has many other appealing properties. We give a complete axiomatic characterization for two step market evaluations. We show further that in a dynamic setting with continuous stock prices every evaluation which is time-consistent and market-consistent is a two step market evaluation. We also give characterization results and examples in terms of g-expectations in a Brownian-Poisson setting.

We consider evaluation methods for payoffs with an inherent financial risk as encountered for instance for portfolios held by pension funds and insurance companies. Pricing such payoffs in a way consistent to market prices typically involves combining actuarial techniques with methods from mathematical finance. We propose to extend standard actuarial principles by a new market-consistent evaluation procedure which we call ‘two step market evaluation.’ This procedure preserves the structure of standard evaluation techniques and has many other appealing properties. We give a complete axiomatic characterization for two step market evaluations. We show further that in a dynamic setting with continuous stock prices every evaluation which is time-consistent and market-consistent is a two step market evaluation. We also give characterization results and examples in terms of g-expectations in a Brownian-Poisson setting.

We consider evaluation methods for payoffs with an inherent financial risk as encountered for instance for portfolios held by pension funds and insurance companies. Pricing such payoffs in a way consistent to market prices typically involves combining actuarial techniques with methods from mathematical finance. We propose to extend standard actuarial principles by a new market-consistent evaluation procedure which we call ‘two step market evaluation.’ This procedure preserves the structure of standard evaluation techniques and has many other appealing properties. We give a complete axiomatic characterization for two step market evaluations. We show further that in a dynamic setting with continuous stock prices every evaluation which is time-consistent and market-consistent is a two step market evaluation. We also give characterization results and examples in terms of g-expectations in a Brownian-Poisson setting.

We examine whether and to what extent joint choices are more or less patient and time-consistent than individual choices in households. We use data from an artefactual field experiment where both individual and joint time preferences were elicited. We find a substantial shift from individual to joint household decisions. Interestingly, joint decisions do not only generate beneficial shifts, i.e., patient and time-consistent shifts. On the contrary, a majority of the observed shifts are impatient and time-inconsistent shifts. A number of observable characteristics are significantly correlated with these shifts in preferences from individual decisions to joint decisions. JEL classification: C91; C92; C93; D10

Paper I: Intra-household Decisions Making on Intertemporal Choices: An Experimental Study in Rural China. In this paper, we conduct an artefactual field experiment in rural China to investigate the determinants of individual and joint decisions regarding intertemporal choices, and estimate the relative influence of spouses on the joint decisions. We use the Convex Time Budget experimental method to elicit both individual and joint decisions on how much money to allocate to an early date and a later date. We find that the rates of return have a significant and positive effect on the allocations to later dates, yet both individual and joint decisions exhibit present-biased time preferences. We also find that both spouses have a significant influence on joint decisions. However, husbands on average have a stronger influence than wives. In particular, the relative patience of husbands significantly increases their relative influence on joint decisions. Although there are few individual and household characteristics related to the relative influence, we do find a link between relative influence in the experiment and households’ decisions on financial savings in real life. Paper II: Choice Shifts in Households: An Experiment on Intertemporal Decisions. In this paper, we investigate choice shifts in households regarding intertemporal choices. In particular, we examine whether and to what extent joint choices are more or less patient and time-consistent than individual choices. We use data from an artefactual experiment conducted by Yang and Carlsson (2012), where the Convex Time Budget experimental method was used to elicit both individual and joint time preferences. We find that 11% of the joint choices are more impatient than the two individual choices, while 9% are more patient. We also find that 17% of joint choice pairs are less time-consistent than the two individual choice pairs, while 12% of the joint choice pairs are more time-consistent. In addition, a number of observable characteristics are significantly correlated with these shifts in preferences from individual decisions to joint decisions. Finally, we also find a significant and consistent pattern between time-consistent/-inconsistent and patient/impatient shifts. Paper III: Are You More Patient and Time-Consistent with Your Spouse’s Money? An Experimental Study with Rural Couples in China. In this paper, we study how partners in a household make decisions for themselves and for their spouses regarding intertemporal choices. In particular, we investigate whether and to what extent the decisions made for the spouse are more or less patient and time-consistent than the subject’s own decisions and predictions of the spouse’s decisions. We conduct an artefactual field experiment with 122 married couples in rural China, and use the Convex Time Budget experimental method to elicit subjects’ time preferences when it comes to own money and spouses’ money as well as the predictions of the spouses’ time preferences. We find that husbands are more patient when making decisions for their wives compared with their predictions of their wives decisions. However, the decisions made for the wives are more patient than the husbands’ own decisions when the choice only involves delayed options. Regardless of the choice involving an immediate option or not, wives’ decisions made for their husbands are similar to the wives’ own decisions and their predictions of the husbands’ decisions. We do not find any evidence that either husbands or wives are significantly more or less time-consistent for their spouses compared with their own decisions and the predictions of their spouses’ decisions. However, highly impatient and time-inconsistent subjects make less impatient and less time-inconsistent decisions for their spouses compared with their own decisions. In contrast, patient and time-consistent subjects make less patient and less time-consistent decisions for their spouses compared with their own decisions. Paper IV: Positional Concern, Gender, and Household Expenditures. This paper uses a survey-based experiment to investigate Chinese farmers’ positional concerns and their determinants. We also examine the correlation between degree of positionality and household expenditures on a set of visible goods. On average, respondents have strong positional concerns for income. In particular, respondents from high-income households are more concerned with their relative position than others. We find a difference between males and females with respect to correlation between degree of positionality and household expenditures on visible goods. For females, there is a positive correlation between degree of positionality and household expenditures on clothes, restaurants, and mobile phones, respectively. For males, there is a positive correlation between degree of positionality and household expenditures on mobile phones. No significant correlation is found for either gender between degree of positionality and household expenditures on vehicles or housing.

We consider evaluation methods for payoffs with an inherent financial risk as encountered for instance for portfolios held by pension funds and insurance companies. Pricing such payoffs in a way consistent to market prices typically involves combining actuarial techniques with methods from mathematical finance. We propose to extend standard actuarial principles by a new marketconsistent evaluation procedure which we call `two step market evaluation.' This procedure preserves the structure of standard evaluation techniques and has many other appealing properties. We give a complete axiomatic characterization for two step market evaluations. We show further that in a dynamic setting with continuous stock prices every evaluation which is time-consistent and market-consistent is a two step market evaluation. We also give characterization results and examples in terms of g-expectations in a Brownian-Poisson setting.

We consider evaluation methods for payoffs with an inherent financial risk as encountered for instance for portfolios held by pension funds and insurance companies. Pricing such payoffs in a way consistent to market prices typically involves combining actuarial techniques with methods from mathematical finance. We propose to extend standard actuarial principles by a new marketconsistent evaluation procedure which we call `two step market evaluation.' This procedure preserves the structure of standard evaluation techniques and has many other appealing properties. We give a complete axiomatic characterization for two step market evaluations. We show further that in a dynamic setting with continuous stock prices every evaluation which is time-consistent and market-consistent is a two step market evaluation. We also give characterization results and examples in terms of g-expectations in a Brownian-Poisson setting.

Despite much work on hedging in incomplete markets, the literature still lacks tractable dynamic hedges in plausible environments. In this article, we provide a simple solution to this problem in a general incomplete-market economy in which a hedger, guided by the traditional minimum-variance criterion, aims at reducing the risk of a non-tradable asset or a contingent claim. We derive fully analytical optimal hedges and demonstrate that they can easily be computed in various stochastic environments. Our dynamic hedges preserve the simple structure of complete-market perfect hedges and are in terms of generalized \Greeks," familiar in risk management applications, as well as retaining the intuitive features of their static counterparts. We obtain our time-consistent hedges by dynamic programming, while the extant literature characterizes either static or myopic hedges, or dynamic ones that minimize the variance criterion at an initial date and from which the hedger may deviate unless she can pre-commit to follow them. We apply our results to the discrete hedging problem of derivatives when trading occurs infrequently. We determine the corresponding optimal hedge and replicating portfolio value, and show that they have structure similar to their complete market counterparts and reduce to generalized Black-Scholes expressions when specialized to the Black-Scholes setting. We also generalize our results to richer settings to study dynamic hedging with Poisson jumps, stochastic correlation and portfolio management with benchmarking.

We consider evaluation methods for payoffs with an inherent financial risk as encountered for instance for portfolios held by pension funds and insurance companies. Pricing such payoffs in a way consistent to market prices typically involves combining actuarial techniques with methods from mathematical finance. We propose to extend standard actuarial principles by a new marketconsistent evaluation procedure which we call `two step market evaluation.' This procedure preserves the structure of standard evaluation techniques and has many other appealing properties. We give a complete axiomatic characterization for two step market evaluations. We show further that in a dynamic setting with continuous stock prices every evaluation which is time-consistent and market-consistent is a two step market evaluation. We also give characterization results and examples in terms of g-expectations in a Brownian-Poisson setting.

In this paper we give an alternative characterization for time-consistent sets of measures in a discrete setting. For each measure \mathbb{P} in a time-consistent set \mathcal{P} we get a distinct set of predictable processes which in return decribe the \mathbb{P} uniquely. This implies we get a one-to-one correspondence between time-consistent sets of measures and sets of predictable processes with specific features.

Economists favor the use of criteria to characterize sustainability. In practice, policy-makers use indicators, i.e., measurements based on the current economic state and decisions, representing given sustainability issues. In this paper, I introduce a criterion characterizing sustainability with indicators and thresholds acting as constraints. I interpret the thresholds as minimal rights to be guaranteed to all generations, and define sustainable trajectories as those satisfying all the constraints at all times. The new criterion is a “generalized” maximin criterion. The approach is applied to a simple production-consumption economy with non-renewable resources. To derive some policy recommendations on the use of indicators to deal with sustainability, I discuss the implications of such a criterion in terms of trade-off between sustainability thresholds, efficiency, and time-consistency. In particular, the resulting problem is time-inconsistent, and sustainability thresholds may be revised over time. Following the time-inconsistent policy based on indicators, with dynamic revision of the thresholds, may, however, result in a sustained utility path, and even in utility growth.

We investigate the problem of minimizing the Average-Value-at-Risk (AVaR τ ) of the discounted cost over a finite and an infinite horizon which is generated by a Markov Decision Process (MDP). We show that this problem can be reduced to an ordinary MDP with extended state space and give conditions under which an optimal policy exists. We also give a time-consistent interpretation of the AVaR τ . At the end we consider a numerical example which is a simple repeated casino game. It is used to discuss the influence of the risk aversion parameter τ of the AVaR τ -criterion.

We consider evaluation methods for payoffs with an inherent financial risk as encountered for instance for portfolios held by pension funds and insurance companies. Pricing such payoffs in a way consistent to market prices typically involves combining actuarial techniques with methods from mathematical finance. We propose to extend standard actuarial principles by a new market-consistent evaluation procedure which we call `two step market evaluation.' This procedure preserves the structure of standard evaluation techniques and has many other appealing properties. We give a complete axiomatic characterization for two step market evaluations. We show further that in a dynamic setting with a continuous stock prices process every evaluation which is time-consistent and market-consistent is a two step market evaluation. We also give characterization results and examples in terms of g-expectations in a Brownian-Poisson setting.

We consider evaluation methods for payoffs with an inherent financial risk as encountered for instance for portfolios held by pension funds and insurance companies. Pricing such payoffs in a way consistent to market prices typically involves combining actuarial techniques with methods from mathematical finance. We propose to extend standard actuarial principles by a new market-consistent evaluation procedure which we call `two step market evaluation.' This procedure preserves the structure of standard evaluation techniques and has many other appealing properties. We give a complete axiomatic characterization for two step market evaluations. We show further that in a dynamic setting with a continuous stock prices process every evaluation which is time-consistent and market-consistent is a two step market evaluation. We also give characterization results and examples in terms of g-expectations in a Brownian-Poisson setting.

We consider evaluation methods for payoffs with an inherent financial risk as encountered for instance for portfolios held by pension funds and insurance companies. Pricing such payoffs in a way consistent to market prices typically involves combining actuarial techniques with methods from mathematical finance. We propose to extend standard actuarial principles by a new market-consistent evaluation procedure which we call `two step market evaluation.' This procedure preserves the structure of standard evaluation techniques and has many other appealing properties. We give a complete axiomatic characterization for two step market evaluations. We show further that in a dynamic setting with a continuous stock prices process every evaluation which is time-consistent and market-consistent is a two step market evaluation. We also give characterization results and examples in terms of g-expectations in a Brownian-Poisson setting.

We consider long-run behavior of agents assessing risk in terms of dynamic convex risk measures or, equivalently, utility in terms of dynamic variational preferences in an uncertain setting. By virtue of a robust representation, we show that all uncertainty is revealed in the limit and agents behave as expected utility maximizer under the true underlying distribution regardless of their initial risk anticipation. In particular, risk assessments of distinct agents converge. This result is a generalization of the fundamental Blackwell-Dubins Theorem, cp. [Blackwell & Dubins, 62], to convex risk. We furthermore show the result to hold in a non -time-consistent environment.

I study a two-period model of nonlinear, information constrained income taxation. It is shown that time-consistent taxation of annual income welfare-dominates time-consistent taxation of lifetime income if preferences are such that stationary allocations are efficient. If uncertainty is taken into account and if state-contingent fiscal policy is not feasible, time-consistent taxation of annual income can also welfare-dominate taxation of lifetime income under commitment. These findings may help in explaining why governments usually tax annual rather than lifetime earnings.

We construct a time-consistent sublinear expectation in the setting of volatility uncertainty. This mapping extends Peng's G-expectation by allowing the range of the volatility uncertainty to be stochastic. Our construction is purely probabilistic and based on an optimal control formulation with path-dependent control sets., Comment: Published in at http://dx.doi.org/10.1214/12-AAP885 the Annals of Applied Probability (http://www.imstat.org/aap/) by the Institute of Mathematical Statistics (http://www.imstat.org)

We consider optimal stopping problems in uncertain environments for an agent assessing utility by virtue of dynamic variational preferences or, equivalently, assessing risk by dynamic convex risk measures. The solution is achieved by generalizing the approach in terms of multiple priors introducing the concept of variational supermartingales and an accompanying theory. To illustrate results, we consider prominent examples: dynamic entropic risk measures and a dynamic version of generalized average value at risk.

We introduce an Absolute (Relative) Time-consistent Axiom of Revealed Preference which characterizes the consistency of a choice function with the property of absolute (relative) time-consistency and impatience. The axiom requires that the absolute (relative) time-consistent and impatient closure of the revealed preference relation does not conflict with the strict revealed preference relation.

This paper provides a theoretical analysis regarding the rationality of suicide attacks from an economist’s point of view. It is argued that although a terrorist gives up future utility from consumption by committing a suicide attack, this loss can be overcompensated by the utility he derives from the attack. Some individual cases of suicide bombers are presentedin order to elucidate the diversity of motivations behind the attacks. We derive conditions under which a rational agent might decide to become a suicide bomber – or to announce the attack and defect later. The paper shows why the decision to commit a suicide attack can be time-inconsistent and what mechanisms might prevent time-inconsistency. Integrating the psychological concepts of cognitive dissonance and terror management theory into our economic analysis, we demonstrate why – although predicted by standard economic theory – defection is a phenomenon rarely observed.We finally present some policy implications. In the light of our analysis, policies that focus on material well-being seem less promising than policies that address non-monetary benefitsof suicide attacks. The paper concentrates on two policy strategies: offering alternatives – with respect to the aims of terrorism as well as the means to attain them – and reducing the information bias – with respect to the availability as well as the access to information., Economics Working Paper Series, 09/106

We consider a group or committee that faces a binary decision under uncertainty. Each member holds some private information. Members agree which decision should be taken in each state of nature, had this been known, but they may attach different values to the two types of mistake that may occur. Most voting rules have a plethora of uninformative equilibria, and informative voting may be incompatible with equilibrium. We analyze an anonymous randomized majority rule that has a unique equilibrium. This equilibrium is strict, votes are informative, and the equilibrium implements the optimal decision with probability one in the limit as the committee size goes to infinity. We show that this also holds for the usual majority rule under certain perturbations of the behavioral assumptions: (i) a slight preference for voting according to one's conviction, and (ii) transparency and a slight preference for esteem. We also show that a slight probability for voting mistakes strengthens the incentive for informative voting.

Stability-oriented European institutions correspond to the general prescriptions of the 'new macroeconomics consensus'. This contribution provides an assessment of the pros and cons of these institutions in terms of macro stabilisation and exchange-rate swings drawing on different scenarios. We argue that the institutions which have been associated with the Euro - limits on public deficits and a conservative central bank - have somewhat jeopardized the efficiency of this new exchange-rate regime. Adaptation of institutions is thus needed: either cooperation or coordination may enhance European welfare.

We study the effects of nominal debt on the optimal sequential choice of monetary policy. When the stock of debt is nominal, the incentive to generate unanticipated inflation increases the cost of the outstanding debt even if no unanticipated inflation episodes occur in equilibrium. Without full commitment, the optimal sequential policy is to deplete the outstanding stock of debt progressively until these extra costs disappear. Nominal debt is therefore a burden on monetary policy, not only because it must be serviced, but also because it creates a time inconsistency problem that distorts interest rates. The introduction of alternative forms of taxation may lessen this burden, if there is enough commtiment to fiscal policy. If there is full commitment to an optimal fiscal policy, then the resulting monetary policy is the Friedman rule of zero nominal interest rates.

We study dynamic monetary risk measures that depend on bounded discrete-time processes describing the evolution of financial values. The time horizon can be finite or infinite. We call a dynamic risk measure time-consistent if it assigns to a process of financial values the same risk irrespective of whether it is calculated directly or in two steps backwards in time. We show that this condition translates into a decomposition property for the corresponding acceptance sets, and we demonstrate how time-consistent dynamic monetary risk measures can be constructed by pasting together one-period risk measures. For conditional coherent and convex monetary risk measures, we provide dual representations of Legendre--Fenchel type based on linear functionals induced by adapted increasing processes of integrable variation. Then we give dual characterizations of time-consistency for dynamic coherent and convex monetary risk measures. To this end, we introduce a concatenation operation for adapted increasing processes of integrable variation, which generalizes the pasting of probability measures. In the coherent case, time-consistency corresponds to stability under concatenation in the dual. For dynamic convex monetary risk measures, the dual characterization of time-consistency generalizes to a condition on the family of convex conjugates of the conditional risk measures at different times. The theoretical results are applied by discussing the time-consistency of various specific examples of dynamic monetary risk measures that depend on bounded discrete-time processes., Electronic Journal of Probability, 11, ISSN:1083-6489

How should taxes, government expenditures, the primary and fiscal surpluses and government liabilities be set over the business cycle? We assume that the government chooses expenditures and taxes to maximize the utility of a representative household, utility is increasing in government expenditures, only distortionary labor income taxes are available, and the cycle is driven by exogenous technology shocks. We first consider the commitment case, and characterize the Ramsey equilibrium. In the case that the utility function is constant elasticity of substitution between private and public consumption and separable between the composite consumption good and leisure, taxes, government expenditures and the primary surplus should all be constant positive fractions of production, and both government liabilities and the fiscal surplus should be positively correlated with production. Then, we relax the commitment assumption, and we show how to determine numerically whether the Ramsey equilibrium can be sustained by the threat to revert to a Markov perfect equilibrium. We find that, for realistic values of the preferences discount factor, the Ramsey equilibrium is sustainable.

How should taxes, government expenditures, the primary and fiscal surpluses and government liabilities be set over the business cycle? We assume that the government chooses expenditures and taxes to maximize the utility of a representative household, utility is increasing in government expenditures, only distortionary labor income taxes are available, and the cycle is driven by exogenous technology shocks. We first consider the commitment case, and characterize the Ramsey equilibrium. In the case that the utility function is constant elasticity of substitution between private and public con- sumption and separable between the composite consumption good and leisure, taxes, government expenditures and the primary surplus should all be constant positive frac- tions of production, and both government liabilities and the fiscal surplus should be positively correlated with production. Then, we relax the commitment assumption, and we show how to determine numerically whether the Ramsey equilibrium can be sustained by the threat to revert to a Markov perfect equilibrium. We find that, for realistic values of the preferences discount factor, the Ramsey equilibrium is sustain- able. Keywords: Fiscal policy, Commitment, Time-consistency, Ramsey equilibrium, Markov perfect equilibria, Sustainable equilibria.