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We prove that the status quo sets induced by the Raiffa Solution to the two-person Bargaining Problem are curves, except when the bargaining domain is rectangular. This property is used in a separate paper by Livne [3] in the axiomatization of the Raiffa Solution. [ABSTRACT FROM AUTHOR]

We give counterexamples for some statements of Borwein and sufficient conditions for the validity of these. [ABSTRACT FROM AUTHOR]

Focuses on the 'Mathematics of Operations Research' periodical. Increase in the annual number of pages; Contribution of the periodical to the study of operations research and management; Information regarding the circulation of the periodical.

In this paper, we consider the linearly constrained composite convex optimization problem, whose objective is a sum of a smooth function and a possibly nonsmooth function. We propose an inexact augmented Lagrangian (IAL) framework for solving the problem. The stopping criterion used in solving the augmented Lagrangian subproblem in the proposed IAL framework is weaker and potentially much easier to check than the one used in most of the existing IAL frameworks/methods. We analyze the global convergence and the nonergodic convergence rate of the proposed IAL framework. Preliminary numerical results are presented to show the efficiency of the proposed IAL framework and the importance of the nonergodic convergence and convergence rate analysis. Funding: The work of Y.-F. Liu was supported in part by National Natural Science Foundation of China (NSFC) [Grants 11631013, 11331012, 11671419, and 11571221] and Beijing Natural Science Foundation [Grant LI72020]. The work of X. Liu was supported in part by NSFC [Grants 11622112, 11471325, 91530204, and 11688101], the National Center for Mathematics and Interdisciplinary Sciences, Chinese Academy of Sciences (CAS), and Key Research Program of Frontier Sciences (QYZDJ-SSW-SYS010), CAS. The work of S. Ma was supported in part by a startup package from the Department of Mathematics at University of California, Davis. Keywords: inexact augmented Lagrangian framework * nonergodic convergence rate * composite convex programming, 1. Introduction In this paper, we consider the linearly constrained composite convex optimization problem [mathematical expression not reproducible] (1) where A [member of] [R.sup.mxn] and b [member of] [R.sup.m]; f(x) [...]

We study a multiperiod network revenue management problem where a seller sells multiple products made from multiple resources with finite capacity in an environment where the underlying demand function is a priori unknown (in the nonparametric sense). The objective of the seller is to simultaneously learn the unknown demand function and dynamically price the products to minimize the expected revenue loss. For the problem where the number of selling periods and initial capacity are scaled by k > 0, it is known that the expected revenue loss of any non-anticipating pricing policy is [OMEGA]([square root of k]). However, there is a considerable gap between this theoretical lower bound and the performance bound of the best-known heuristic control in the literature. In this paper, we propose a nonparametric self-adjusting control and show that its expected revenue loss is O([k.sup.1/2+[member of]] log k) for any arbitrarily small [member of] > 0, provided that the underlying demand function is sufficiently smooth. This is the tightest bound of its kind for the problem setting that we consider in this paper, and it significantly improves the performance bound of existing heuristic controls in the literature. In addition, our intermediate results on the large deviation bounds for spline estimation and nonparametric stability analysis of constrained optimization are of independent interest and are potentially useful for other applications. Supplemental Material: The online appendix is available at https://doi.org/10.1287/moor.2018.0937. Keywords: revenue management * learning * self-adjusting control * spline approximation * asymptotic analysis, 1. Introduction Revenue management (RM), which was first implemented in the 1960s by legacy airline companies to maintain their edge in the competitive airline market, has recently become widespread in [...]

This paper deals with undiscounted infinite stage two-person zero-sum stochastic games with finite state and action spaces. It was recently shown that such games possess a value. But in general there are no optimal strategies. We prove that for each player there exists a nonempty set of easy initial states, i.e. starting states for which the player possesses an optimal stationary strategy. This result is proved with the aid of facts derived by Bewley and Kohlberg for the limit discount equation for stochastic games. [ABSTRACT FROM AUTHOR]

In this paper, we aim to prove the linear rate convergence of the alternating direction method of multipliers (ADMM) for solving linearly constrained convex composite optimization problems. Under a mild calmness condition, which holds automatically for convex composite piecewise linear-quadratic programming, we establish the global Q-linear rate of convergence for a general semi-proximal ADMM with the dual step-length being taken in (0, (1 +[5.sup.1/2 ])/2). This semi-proximal ADMM, which covers the classic one, has the advantage to resolve the potentially nonsolvability issue of the sub-problems in the classic ADMM and possesses the abilities of handling the multi-block cases efficiently. We demonstrate the usefulness of the obtained results when applied to two- and multi-block convex quadratic (semidefinite) programming. Funding: The research of the first author was supported by the National Natural Science Foundation of China [Projects 11625105 and 11431002]; the research of the second author was supported in part by the Academic Research Fund [Grant R-146-000-207-112]; and the research of the third author was supported by the National Natural Science Foundation of China [Projects 11571059 and 91330206]. Keywords: ADMM * calmness * Q-linear convergence * multiblock * composite conic programming, 1. Introduction In this paper, we shall study the Q-linear rate convergence of the alternating direction method of multipliers (ADMM) for solving the following convex composite optimization problem: min{[?](y + [...]

In this paper, we provide a flexible framework allowing for a unified study of time consistency of risk measures and performance measures (also known as acceptability indices). The proposed framework not only integrates existing forms of time consistency, but also provides a comprehensive toolbox for analysis and synthesis of the concept of time consistency in decision making. In particular, it allows for in-depth comparative analysis of (most of) the existing types of time consistency--a feat that has not been possible before and, which is done in the companion paper by the authors. In our approach, the time consistency is studied for a large class of maps that are postulated to satisfy only two properties--monotonicity and locality. We call these maps LM-measures. The time consistency is defined in terms of an update rule. The form of the update rule introduced here is novel, and is perfectly suited for developing the unifying framework that is worked out in this paper. As an illustration of the applicability of our approach, we show how to recover almost all concepts of weak time consistency by means of constructing appropriate update rules. Funding: The first and second author acknowledge support from the National Science Foundation [Grant DMS-1211256]. The third author acknowledges support by project operated within the Foundation for Polish Science IPP Programme 'Geometry and Topology in Physical Model,' cofinanced by the EU European Regional Development Fund, Operational Program Innovative Economy 2007-2013. Keywords: time consistency * update rule * dynamic LM-measure * dynamic risk measure * dynamic acceptability index * dynamic performance measure, 1. Introduction In the seminal paper by Artzner et al. [3], the authors proposed an axiomatic approach to defining risk measures that are meant to give a numerical value of [...]

In management and planning it is commonplace for additional information to become available gradually over time. It is well known that most risk measures (risk functionals) are time inconsistent in [...]

In this paper we provide a complete theoretical analysis of a two-dimensional degenerate nonconvex singular stochastic control problem. The optimisation is motivated by a storage-consumption model in an electricity market, and features a stochastic real-valued spot price modelled by Brownian motion. We find analytical expressions for the value function, the optimal control, and the boundaries of the action and inaction regions. The optimal policy is characterised in terms of two monotone and discontinuous repelling free boundaries, although part of one boundary is constant and the smooth fit condition holds there. Funding: The first and the third authors were supported by the Engineering and Physical Sciences Research Council (EPSRC) [Grant EP/K00557X/1]. Financial support by the German Research Foundation (DFG) through the Collaborative Research Centre 'Taming uncertainty and profiting from randomness and low regularity in analysis, stochastics and their applications' is gratefully acknowledged by the second author. Keywords: finite-fuel singular stochastic control * optimal stopping * free boundary * Hamilton-Jacobi-Bellman equation * irreversible investment * electricity market, 1. Introduction Consider the following problem introduced in De Angelis et al. [4]: a firm purchases electricity over time at a stochastic spot price [([X.sub.t]).sub.t[greater than or equal to]0] for [...]

This paper studies curves of the form [([rho]([lambda]X)).sub.[lambda][greater than or equal to]0], called risk profiles, where [rho] is a convex risk measure and X a random variable. Financially, this captures the sensitivity of risk to the size of the investment in X, which the original axiomatic foundations of convex risk measures suggest to interpret as liquidity risk. The shape of a risk profile is intimately linked with the tail behavior of X for some notable classes of risk measures, namely shortfall risk measures and optimized certainty equivalents, and shares many useful features with cumulant generating functions. Exploiting this link leads to tractable necessary and sufficient conditions for pointwise bounds on risk profiles, which we call concentration inequalities. These inequalities admit useful dual representations related to transport inequalities, and this leads to efficient uniform bounds for risk profiles for large classes of X. Several interesting mathematical results emerge from this analysis, including a new perspective on nonexponential concentration estimates and some peculiar characterizations of classical transport inequalities. Lastly, the analysis is deepened by means of a surprising connection between time consistency properties of law invariant risk measures and the tensorization of concentration inequalities. Funding: This research is supported by the National Science Foundation [Award DMS-1502980]. Keywords: convex risk measures * liquidity risk * concentration of measure * transport inequalities, 1. Introduction Throughout the paper, a risk measure is a convex functional [rho] acting on random variables satisfying the following axioms: 1. Normalization: [rho](0) = 0. 2. Cash additivity: [rho](X [...]

In this paper, we consider the optimal dividend payment strategy for an insurance company that has two collaborating business lines. The surpluses of the business lines are modeled by diffusion processes. The collaboration between the two business lines permits that money can be transferred from one line to another with or without proportional transaction costs, while money must be transferred from one line to another to help both business lines keep running before simultaneous ruin of the two lines eventually occurs. Keywords: optimal dividends strategy * diffusion model * collaborating businesses * stochastic control, 1. Introduction This paper is concerned with a classical problem of actuarial mathematics, strategies for optimal payout of dividends when two collaborating lines of business are taken into account. Since [...]

In this paper, we consider a finite-horizon Markov decision process (MDP) for which the objective at each stage is to minimize a quantile-based risk measure (QBRM) of the sequence of future costs; we call the overall objective a dynamic quantile-based risk measure (DQBRM). In particular, we consider optimizing dynamic risk measures where the one-step risk measures are QBRMs, a class of risk measures that includes the popular value at risk (VaR) and the conditional value at risk (CVaR). Although there is considerable theoretical development of risk-averse MDPs in the literature, the computational challenges have not been explored as thoroughly. We propose data-driven and simulation-based approximate dynamic programming (ADP) algorithms to solve the risk-averse sequential decision problem. We address the issue of inefficient sampling for risk applications in simulated settings and present a procedure, based on importance sampling, to direct samples toward the 'risky region' as the ADP algorithm progresses. Finally, we show numerical results of our algorithms in the context of an application involving risk-averse bidding for energy storage. Supplemental Material: The online appendix is available at https://doi.org/10.1287/moor.2017.0872. Keywords: approximate dynamic programming * dynamic risk measures * energy trading * reinforcement learning * Q-learning, 1. Introduction Sequential decision problems, in the form of Markov decision processes (MDPs), are most often formulated with the objective of minimizing an expected sum of costs or maximizing an [...]

Scheduling control for a single-server queue with I customer classes and reneging is considered, with linear holding or reneging cost. An asymptotically optimal (AO) policy in heavy traffic is identified where classes are prioritized according to a workload-dependent dynamic index rule. Denote by [c.sub.i], [[mu].sub.i], and [[theta].sub.i], i [member of] I := {1,..., 1} the queue length cost, service rate, and reneging rate, for class-i customers. Then, a relabeling of the classes and a partition 0 = [w.sub.0] < [w.sub.1] < ... < [w.sub.K] = [infinity], K [greater than or equal to] I are identified such that the policy acts to always assign least priority to the class i when the rescaled workload is in the interval [[w.sub.i-1], [w.sub.i]). The relabeling is such that when workload is withing the lowest [resp., highest] interval [[w.sub.i-1], [w.sub.i]), the least priority class is the one with smallest c[mu] [resp., greatest [theta]] value. This result stands in sharp contrast to known fluid-scale results where it is AO to prioritize by the fixed c[mu]/[theta] index. One of the technical challenges is the discontinuity of the limiting queue length process under optimality. Discontinuities occur whenever the workload reaches one of the levels [w.sub.i]. Funding: This research was supported in part by the Israel Science Foundation [Grant 1315/12]. Keywords: multiclass single-server queue * queues with abandonment * diffusion control problem * Bellman equation * dynamic priorities * state-space collapse, 1. Introduction In this paper, we address asymptotically optimal (AO) scheduling control for the multiclass single-server queue with abandonment in heavy traffic. We show that, in sharp contrast to the [...]

This paper studies the dynamic portfolio choice problem with ambiguous jump risks in a multidimensional jump-diffusion framework. We formulate a continuous-time model of incomplete market with uncertain jumps. We develop an efficient pathwise optimization procedure based on the martingale methods and minimax results to obtain closed-form solutions for the indirect utility function and the probability of the worst scenario. We then introduce an orthogonal decomposition method for the multidimensional problem to derive the optimal portfolio strategy explicitly under ambiguity aversion to jump risks. Finally we calibrate our model to real market data drawn from 10 international indices and illustrate our results by numerical examples. The certainty equivalent losses affirm the importance of jump uncertainty in optimal portfolio choice. Funding: Dan Luo was supported, in part, by the Natural Science Foundation of China [Grant 71302075/G0206]. Xudong Zeng was supported, in part, by the Natural Science Foundation of China [Grant 71271127/G0115]. Keywords: optimal investment * ambiguity aversion * duality method * jump diffusion * worst-case scenario, 1. Introduction A number of empirical and theoretical studies have demonstrated that jump risks have a substantial impact on optimal portfolio formation. For example, in a single-stock double-jump model, Liu [...]

In this paper, we present an analysis of the strength of sparse cutting planes for mixed integer linear programs (MILP) with sparse formulations. We examine three kinds of problems: packing problems, covering problems, and more general MILPs with the only assumption that the objective function is nonnegative. Given an MILP instance of one of these three types, assume that we decide on the support of cutting planes to be used and the strongest inequalities on these supports are added to the linear programming relaxation. We present bounds on the ratio of optimal value of the LP relaxation after adding cuts and the optimal value of the MILP that depends only on the sparsity structure of the constraint matrix and the support of sparse cuts selected, that is, these bounds are completely data independent. These results also shed light on the strength of single-scenario cuts for two-stage stochastic MILPs. Funding: The first and third author acknowledge the support from National Science Foundation [Grants CCF 1415460 and CMMI 1149400]. The second author acknowledges the support from CNPq [Grant Universal 431480/2016-8]. Keywords: cutting planes * mixed-integer linear programming * sparsity, 1. Introduction 1.1. Motivation and Goal Cutting plane technology has become one of the main pillars in the edifice that is a modern state-of-the-art mixed integer linear programming (MILP) solver. [...]

We apply a new method of analysis to the asymmetric rendezvous search problem on the line (ARSPL). This problem, previsouly studied in a paper of Alpern and Gal (1995), asks how two blind, speed one players placed a distance d apart on the line, can find each other in minimum expected time. The distance d is drawn from a known cumulative probability distribution G, and players are faced in random directions. We show that the ARSPL is strategically equivalent to a new problem we call the double linear search problem (DLSP), where an object is placed equiprobably on one of two lines, and equiprbably at position ±d. A searcher is placed at the origin of each of these lines. The two searcher move with a combined speed of one, of minimize the expected time before one of them finds the object. Using results from a concurrent paper of the first author and J. V. Howard (1998), we solve the DLSP (and hence the ARSPL) for the case where G is convex on its support, and shown that the solution is that conjectured in a paper of Baston and Gal(1998). [ABSTRACT FROM AUTHOR]

The concept of ambiguity designates those situations where the information available to the decision maker is insufficient to form a probabilistic view of the world. Thus, it has provided the motivation for departing from the subjective expected utility (SEU) paradigm. Yet, the formalization of the concept is missing. This is a grave omission as it leaves nonexpected utility models hanging on shaky ground. In particular, it leaves unanswered basic questions such as the following: (1) Does ambiguity exist? (2) If so, which situations should be labeled as "ambiguous"? (3) Why should one depart from SEU in the presence of ambiguity? (4) If so, what kind of behavior should emerge in the presence of ambiguity? The present paper fills these gaps. Specifically, it identifies those information structures that are incompatible with SEU theory, and shows that their mathematical properties are the formal counterpart of the intuitive idea of insufficient information. These are used to give a formal definition of ambiguity and, consequently, to distinguish between ambiguous and unambiguous situations. Finally, the paper shows that behavior not conforming to SEU theory must emerge in correspondence of insufficient information and identifies the class of non-EU models that emerge in the face of ambiguity. The paper also proposes a new comparative definition of ambiguity, and discusses its relation with some of the existing literature. Funding: Financial support from the Social Sciences and Humanities Research Council of Canada [Grant 410-2011-2025] is gratefully acknowledged. Keywords: nonexpected utility * information * ambiguity * Choquet integral, 1. Introduction The past few years have witnessed an ever-increasing number of applications of nonexpected utility (non-EU) theories. This has been favored both by the recent theoretical developments and by [...]

This paper examines a Markovian model for the optimal irreversible investment problem of a firm aiming at minimizing total expected costs of production. We model market uncertainty and the cost of investment per unit of production capacity, as two independent one-dimensional regular diffusions, and we consider a general convex running cost function. The optimization problem is set as a three-dimensional degenerate singular stochastic control problem. We provide the optimal control as the solution of a reflected diffusion at a suitable boundary surface. Such boundary arises from the analysis of a family of two-dimensional parameter-dependent optimal stopping problems, and it is characterized in terms of the family of unique continuous solutions to parameter-dependent, nonlinear integral equations of Fredholm type. Funding: The first author was supported by Engineering and Physical Sciences Research Council [Grant EP/K00557X/1]. The second author thankfully acknowledges the financial support by the German Academic Exchange Service (DAAD). The third author gratefully acknowledges the financial support by the German Research Foundation (DFG) [Grant Ri-1128-4-2]. Keywords: irreversible investment * singular stocliastic control * optimal stopping * free-boundary problems * nonlinear integral equations, 1. Introduction In this paper, we study a Markovian model for a firm's optimal irreversible investment problem. The firm aims at minimizing total expected costs of production when its running [...]

In this paper, we consider a class of constrained optimization problems where the feasible set is a general closed convex set, and the objective function has a nonsmooth, nonconvex regularizer. Such a regularizer includes widely used SCAD, MCP, logistic, fraction, hard thresholding, and non-Lipschitz [L.sub.p] penalties as special cases. Using the theory of the generalized directional derivative and the tangent cone, we derive a first order necessary optimality condition for local minimizers of the problem, and define the generalized stationary point of it. We show that the generalized stationary point is the Clarke stationary point when the objective function is Lipschitz continuous at this point, and satisfies the existing necessary optimality conditions when the objective function is not Lipschitz continuous at this point. Moreover, we prove the consistency between the generalized directional derivative and the limit of the classic directional derivatives associated with the smoothing function. Finally, we establish a lower bound property for every local minimizer and show that finding a global minimizer is strongly NP-hard when the objective function has a concave regularizer. Funding: The work in the present paper was supported by the Natural Science Foundation of China [Grants 11471088, 61403101], HIT.BRETIII.201414, PIRS of HIT No.A201402, PIRS of HIT No.B201501, and partly by Hong Kong Research Grant Council [Grant PolyU5002/13P]. Keywords: constrained nonsmooth nonconvex optimization [??] optimality condition [??] generalized directional derivative [??] directional derivative consistency [??] numerical property, 1. Introduction In this paper, we consider the following constrained optimization problem: [mathematical expression not reproducible] (1) where [THETA]: [R.sup.n] [right arrow] R and c: [R.sup.m] [right arrow] R are [...]

Often in applications such as rare events estimation or optimal control it is required that one calculates the principal eigenfunction and eigenvalue of a nonnegative integral kernel. Except in the finite-dimensional case, usually neither the principal eigenfunction nor the eigenvalue can be computed exactly. In this paper, we develop numerical approximations for these quantities. We show how a generic interacting particle algorithm can be used to deliver numerical approximations of the eigenquantities and the associated so-called "twisted" Markov kernel as well as how these approximations are relevant to the aforementioned applications. In addition, we study a collection of random integral operators underlying the algorithm, address some of their mean and pathwise properties, and obtain error estimates. Finally, numerical examples are provided in the context of importance sampling for computing tail probabilities of Markov chains and computing value functions for a class of stochastic optimal control problems. Keywords: interacting particle methods * eigenfunctions * rare events estimation * optimal control * diffusion Monte Carlo, 1. Introduction On a state space X consider a bounded function G: X -[much greater than] [R.sub.+], a Markov probability kernel M. The central object of interest in this paper [...]

Calculating optimal policies is known to be computationally difficult for Markov decision processes (MDPs) with Borel state and action spaces. This paper studies finite-state approximations of discrete time Markov decision processes with Borel state and action spaces, for both discounted and average costs criteria. The stationary policies thus obtained are shown to approximate the optimal stationary policy with arbitrary precision under quite general conditions for discounted cost and more restrictive conditions for average cost. For compact-state MDPs, we obtain explicit rate of convergence bounds quantifying how the approximation improves as the size of the approximating finite state space increases. Using information theoretic arguments, the order optimality of the obtained convergence rates is established for a large class of problems. We also show that as a pre-processing step, the action space can also be finitely approximated with sufficiently large number points; thereby, well known algorithms, such as value or policy iteration, Q-learning, etc., can be used to calculate near optimal policies. Funding: This research was supported in part by the Natural Sciences and Engineering Research Council (NSERC) of Canada. Keywords: Markov decision processes [??] stochastic control [??] finite state approximation [??] quantization, 1. Introduction In this paper, our goal is to study the finite-state approximation problem for computing near optimal policies for discrete time Markov decision processes (MDPs) with Borel state and [...]

In this paper we extend the framework of the evolutionary inspection game put forward recently by the author and coworkers to a large class of conflict interactions to address the pressure executed by the major player (or principal) on the large group of small players who can resist this pressure or collaborate with the major player. We prove rigorous results on the convergence of various Markov decision models of interacting small agents (including evolutionary growth), i.e., pairwise, in groups and by coalition formation, to a deterministic evolution on the distributions of the state spaces of small players paying main attention to situations with an infinite state-space of small players. We supply precise rates of convergence. The theoretical results of the paper are applied to the analysis of the processes of inspection, corruption, cyber-security, counter-terrorism, banks and firms merging, strategically enhanced preferential attachment, and many other. Keywords: inspection * corruption * cyber-security * crime prevention * geopolitics * counterterrorism * optimal allocation * evolutionary game * major player * coalition growth * pressure and resistance * social norms * networking * law of large numbers * strategically enhanced preferential attachment, 1. Introduction 1.1. Objectives and Content of the Study The inspection games represent an important class of games with various applications from the arms race control to the study of [...]

Randomizing (stochastic) global optimization algorithms can be viewed as sampling procedures, where at each iteration a local optimum is sampled from the set of local optima. The effectiveness of such an algorithm depends crucially on the sampling distribution, i.e., on the probabilities of sampling the various local optima. There exists a very large body of research on stochastic global optimization. However, very little is known about the sampling distribution itself and, in particular, on the specific way in which it depends on the function being optimized, on the region in which the search takes place, and on the optimization routine. In this paper we set out to examine these issues in some detail and present some first results in this direction. The case analyzed in this paper is the optimization of a one-dimensional function using a randomizing version of binary search. We give an effective (computable in quadratic time) formula for the sampling distribution and obtain various interesting properties of this distribution which are relevant to the behavior of the algorithm in practice. We also discuss some issues related to adaptive search. [ABSTRACT FROM AUTHOR]

Mathematical models for multistate reliability systems of multistate components have been proposed by Barlow and Wu (1978), El-Neweihi et al. (1978) and Griffith (1980). Unlike the approach used by Barlow and Wu, the other authors preferred to establish their classes of models through sets of axioms extending the early binary notions and containing as special cases the class of models suggested by Barlow and Wu. Since the Barlow and Wu approach is set theoretic and the model definition is essentially qualitative, a question of interest concerns its axiomatic characterization among larger classes of models. In this paper such a characterization is established that relates the Barlow and Wu models to the other classes of models introduced later. [ABSTRACT FROM AUTHOR]

In this paper we show that if Z is a partially ordered linear space with the property that each set with an upper bound has a least upper bound, then any convex operator F from a linear space X into Z has a support at each x∈X(i.e., for each x∈X, there exists an affine operator A such that A(x)=F(x) and A(y) ≤ F(Y) for each y∈X. The results in this paper are actually in the context of a more general condition than convexity, called W-convexity. W-convexity is a pointwise property of an operator and is closely related to another generalization of convexity, called order-convexity, which was introduced by Ortega and Rheinboldt in 1967. [ABSTRACT FROM AUTHOR]

The discussion below, from Karen Aardal and Arjen K. Lenstra, represents correction of an error made in their paper, Aardal, Karen, Arjen K. Lenstra. 2004. Hard equality constrained integer knapsacks. [...]

This paper considers a portfolio management problem of Merton's type in which the risky asset return is related to the return history. The problem is modeled by a stochastic system with delay. The investor's goal is to choose the investment control as well as the consumption control to maximize his total expected, discounted utility. Under certain situations, we derive the explicit solutions in a finite dimensional space. Key words: stochastic delay equations; optimal stochastic control; Hamilton-Jacobi-Bellman equation MSC2000 subject classification: Primary: 34K50, 91B28; secondary: 93E20, 49L20 OR/MS subject classification: Primary: dynamic programming/optimal control-applications; secondary: finance-portfolio, investment History: Received April 1, 2010; revised February I. 2011. Published online in Articles in Advance October 14, 2011., 1. Introduction. In this paper, we consider a stochastic portfolio management problem in which the history (delay) of the portfolio performance is taken into consideration. In the classical Merton's model, [...]

The paper concerns the computation of the graphical derivative and the regular (Frechet) coderivative of the normalcone mapping related to [C.sup.2] inequality constraints under very weak qualification conditions. This enables [...]

This paper is concerned with optimal switching over multiple modes in continuous time and on a finite horizon. The performance index includes a running reward, terminal reward, and switching costs [...]

This paper introduces a class of contest models in which each player decides when to stop a privately observed Brownian motion with drift and incurs costs depending on his stopping [...]

Two important characteristics encountered in many real-world scheduling problems are heterogeneous processors and a certain degree of uncertainty about the processing times of jobs. In this paper we address both, [...]

In this paper we characterize the 'price of anarchy,' i.e., the inefficiency between user and system optimal solutions, when costs are nonseparable, asymmetric and nonlinear, generalizing earlier work that has [...]

In this paper we introduce a novel flow representation for finite games in strategic form. This representation allows us to develop a canonical direct sum decomposition of an arbitrary game into three components, which we refer to as the potential, harmonic, and nonstrategic components. We analyze natural classes of games that are induced by this decomposition, and in particular, focus on games with no harmonic component and games with no potential component. We show that the first class corresponds to the well-known potential games. We refer to the second class of games as harmonic games, and demonstrate that this new class has interesting properties which contrast with properties of potential games. Exploiting the decomposition framework, we obtain explicit expressions for the projections of games onto the subspaces of potential and harmonic games. This enables an extension of the equilibrium properties of potential and harmonic games to "nearby" games. [ABSTRACT FROM AUTHOR]

In the paper we consider the chance-constrained version of an affinely perturbed linear matrix inequality (LMI) constraint, assuming the primitive perturbations to be independent with light-tail distributions (e.g., bounded or Gaussian). Constraints of this type, playing a central role in chance-constrained linear/conic quadratic/semidefinite programming, are typically computationally intractable. The goal of this paper is to develop a tractable approximation to these chance constraints. Our approximation is based on measure concentration results and is given by an explicit system of LMIs. Thus, the approximation is computationally tractable; moreover, it is also safe, meaning that a feasible solution of the approximation is feasible for the chance constraint. [ABSTRACT FROM AUTHOR]

A decision maker is engaged in a repeated interaction with Nature. The objective of the decision maker is to guarantee to himself the average payoff as large as the best-reply payoff to Nature's empirical distribution of play, no matter what Nature does. The decision maker with perfect recall can achieve this objective by a simple better-reply strategy. In this paper we demonstrate that the relationship between perfect recall and bounded recall is not straightforward: The decision maker with bounded recall may fail to achieve this objective, no matter how long his recall and no matter what better-reply strategy he uses. [ABSTRACT FROM AUTHOR]

This paper is concerned with the optimality of a trend following trading rule. The underlying market is modeled like a bull-bear switching market in which the drift of the stock [...]

In a recent paper Li and Singer (1998) introduced the notion of global error bound for a convex multifunction at a point of its domain. They showed the existence of such a global error bound when the image of the multifunction at the respective point is bounded and conjectured a result for the case when the image is not bounded. In this paper we solve their conjecture with a positive answer. For this we establish a criterion for the existence of a global error bound using the Pompeiu-Hausdorff excess. We also improve slightly some results of Li and Singer and introduce a gage associated to a multifunction similar to that for well-conditioning of convex functions, with similar properties. [ABSTRACT FROM AUTHOR]

The paper addresses a class of continuous-time, optimal control problems whose solutions are typically characterized by both bang-bang and "singular" control regimes. Analytical study and numerical computation of such solutions are very difficult and far from complete when only techniques from control theory are used. This paper solves optimal control problems by reducing them to the combinatorial search for the shortest path in a specially constructed graph. Since the nodes of the graph are weighted in a sequence-dependent manner, we extend the classical, shortest-path algorithm to our case. The proposed solution method is currently limited to single-state problems with multiple control functions. A production planning problem and a train operation problem are optimally solved to illustrate the method. [ABSTRACT FROM AUTHOR]

Stochastic billiards can be used for approximate sampling from the boundary of a bounded convex set through the Markov Chain Monte Carlo paradigm. This paper studies how many steps of [...]

This paper compares two frameworks for measuring risk in a multiperiod setting. The first corresponds to applying a single coherent risk measure to the cumulative future costs, and the second [...]

This paper studies a problem of Bayesian parameter estimation for a sequence of scaled counting processes whose weak limit is a Brownian motion with an unknown drift. The main result [...]

This paper considers the use of a simple posterior sampling algorithm to balance between exploration and exploitation when learning to optimize actions such as in multiarmed bandit problems. The algorithm, [...]

In two-sided matching markets, the concept of stability proposed by Gale and Shapley is one of the most important solution concepts. In this paper, we consider a problem related to [...]

In this paper, we introduce a notion to be called A-wise uncorrelated random variables, which is similar but not identical to the so-called k-wise independent random variables in the literature. [...]

This paper considers infinite-horizon finite state-and-action Markov population decision chains (MPDCs) in which the goal is to find a stationary stopping policy with maximum stopping value, that is, with maximum [...]

The nonlinear complementarity problem has been converted into a system of nonsmooth equations by means of Fischer-Burmeister functional, which may be called the Fischer-Burmeister equation. The local superlinear convergence of the generalized Newton method applied to the Fischer- Burmeister equation has been established under certain regularity assumptions. In contrast to the damped Newton method for systems of smooth equations, global convergence of the damped generalized Newton method for systems of nonsmooth equations cannot be proved in general. In this paper, we show that the natural globalization of the Newton method for smooth equations can be extended to the Fischer-Burmeister equation without any hybrid strategy. Moreover, we are also able to demonstrate that the damped modified Gauss-Newton method can be extended to the Fischer- Burmeister equation. This shows that the elegant convergence analysis of the traditional Newton, damped Newton and damped Gauss-Newton methods can be naturally generalized to the Fischer- Burmeister equation. [ABSTRACT FROM AUTHOR]

We study convex optimization problems for which the data is not specified exactly and it is only known to belong to a given uncertainty set U, yet the constraints must hold for all possible values of the data from U. The ensuing optimization problem is called robust optimization. In this paper we lay the foundation of robust convex optimization. In the main part of the paper we show that if U is an ellipsoidal uncertainty set, then for some of the most important generic convex optimization problems (linear programming, quadratically constrained programming, semidefinite programming and others) the corresponding robust convex program is either exactly, or approximately, a tractable problem which lends itself to efficient algorithms such as polynomial time interior point methods. [ABSTRACT FROM AUTHOR]

This paper compares solution concepts associated with three location problems on a network: (i) a single-facility distance minimization problem; (ii) a two-facility spatial competition problem; and (iii) a single-facility locational voting problem. It is shown that the three problems have a common global solution when the network exhibits a property of symmetry around a point. For more general networks, this ceases to be true for global solutions but an identity holds for local solutions. [ABSTRACT FROM AUTHOR]