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We study an optimal investment and consumption problem with heterogeneous consumption of basic and luxury goods, together with the choice of time for retirement. The optimal heterogeneous consumption strategies for a class of nonhomothetic utility maximizer are shown to consume only basic goods when the wealth is small, to consume basic goods and make savings when the wealth is intermediate, and to consume almost all in luxury goods when the wealth is large. The optimal retirement policy is shown to be both universal, in the sense that all individuals should retire at the same level of marginal utility that is determined only by income, labor cost, discount factor as well as market parameters, and not universal, in the sense that all individuals can achieve the same marginal utility with different utility and wealth. We also show that individuals prefer to retire as time goes by if the marginal labor cost increases faster than that of income. This paper studies an optimal investment and consumption problem with heterogeneous consumption of basic and luxury goods, together with the choice of time for retirement. The utility for luxury goods is not necessarily a concave function. The optimal heterogeneous consumption strategies for a class of nonhomothetic utility maximizer are shown to consume only basic goods when the wealth is small, to consume basic goods and make savings when the wealth is intermediate, and to consume almost all in luxury goods when the wealth is large. The optimal retirement policy is shown to be both universal, in the sense that all individuals should retire at the same level of marginal utility that is determined only by income, labor cost, discount factor and market parameters, and not universal, in the sense that all individuals can achieve the same marginal utility with different utility and wealth. It is also shown that individuals prefer to retire as time goes by if the marginal labor cost increases faster than that of income. The main tools used in analyzing the problem are from a partial differential equation and stochastic control theory including variational inequality and dual transformation. We finally conduct the simulation analysis for the featured model parameters to investigate practical and economic implications by providing their figures. Funding: This work was supported by Hong Kong Research Grants Council General Research Fund [Grants 15202421 and 15202817], the National Research Foundation of Korea [Grant 2021R1C1C1004647], the PolyU-SDU Joint Research Center on Financial Mathematics, the CAS AMSS-PolyU Joint Laboratory of Applied Mathematics, and Hong Kong Polytechnic University, the National Natural Science Foundation of China [Grant 11971409], and the Engineering and Physical Sciences Research Council (UK) [Grant EP/V008331/1]. Supplemental Material: The online appendix is available at https://doi.org/10.1287/opre.2022.2328. [ABSTRACT FROM AUTHOR]

Portfolio risk taking when periodic performance matters Incentives of portfolio managers in real life are typically tied to their periodic performance—a criterion that has received very little attention to date. How does the repeated nature of the rewards influence the portfolio managers' trading strategies? Tse and Zheng address this question via a dynamic model of investment in "Portfolio selection, periodic evaluations, and risk taking." The return benchmark of the periodic evaluations plays a crucial role. A reasonable benchmark in conjunction with periodic payouts can mitigate excessive risk taking during market downturns. However, an overly aggressive benchmark could result in limited portfolio growth as well as ruin risk over the long run. The theoretical findings yield policy implications over incentives management and remuneration structure design to better align the short-term periodic interest of the portfolio managers and the long-term performance goal of the stakeholders. We present a continuous-time portfolio selection problem faced by an agent with S-shaped preference who maximizes the utilities derived from the portfolio's periodic performance over an infinite horizon. The periodic reward structure creates subtle incentive distortion. In some cases, local risk aversion is induced, which discourages the agent from risk taking in the extreme bad states of the world. In some other cases, eventual ruin of the portfolio is inevitable, and the agent underinvests in the good states of the world to manipulate the basis of subsequent performance evaluations. We outline several important elements of incentive design to contain the long-term portfolio risk. Funding: H. Zheng is supported in part by the Engineering and Physical Sciences Research Council [Grant EP/V00833/1]. Supplemental Material: The e-companion is available at https://doi.org/10.1287/opre.2021.0780. [ABSTRACT FROM AUTHOR]

We establish a rigorous duality theory, under No Unbounded Profit with Bounded Risk, for an infinite horizon problem of optimal consumption in the presence of an income stream that can terminate randomly at an exponentially distributed time, independent of the asset prices. We thus close a duality gap encountered in the Davis‐Vellekoop example in a version of this problem in a Black‐Scholes market. Many of the classical tenets of duality theory hold, with the notable exception that marginal utility at zero initial wealth is finite. We use as dual variables a class of supermartingale deflators such that deflated wealth plus cumulative deflated consumption in excess of income is a supermartingale. We show that the space of discounted local martingale deflators is dense in our dual domain, so that the dual problem can also be expressed as an infimum over the discounted local martingale deflators. We characterize the optimal wealth process, showing that optimal deflated wealth is a potential decaying to zero, while deflated wealth plus cumulative deflated consumption over income is a uniformly integrable martingale at the optimum. We apply the analysis to the Davis‐Vellekoop example and give a numerical solution. [ABSTRACT FROM AUTHOR]

In this paper we introduce a general framework for time-inconsistent optimal control problems. We characterize the closed-loop equilibrium strategy in both the integral and pointwise forms with the newly developed methodology. We recover and improve the results of some wellknown models, including the classical optimal control, Bjork, Khapko, and Murgoci [Finance Stoch., 21 (2017), pp. 331-360], He and Jiang, preprint, ssrn:3308274, 2020, and Yong [Math. Control Related Fields, 2 (2012), pp. 271-329] models, and reveal some interesting aspects that appear for the first time in the literature. We illustrate the usefulness of the model and the results by a number of examples in dynamic portfolio selection, including mean-variance with state-dependent risk aversion, investment/consumption with nonexponential discounting, and utility-deviation-risk with coupled terminal state and expected terminal state. [ABSTRACT FROM AUTHOR]

In this paper, we study a continuous time structural asset value model for two correlated firms using a two-dimensional Brownian motion. We consider the situation of incomplete information, where the information set available to the market participants includes the default time of each firm and the periodic asset value reports. In this situation, the default time of each firm becomes a totally inaccessible stopping time to the market participants. The original structural model is first transformed to a reduced-form model. Then the conditional distribution of the default time together with the asset value of each name are derived. We prove the existence of the intensity processes of default times and also give the explicit form of the intensity processes. Numerical studies on the intensities of the two correlated names are conducted for some special cases. [ABSTRACT FROM AUTHOR]

We consider portfolio optimization problems with expected loss constraints under the physical measure P and the risk neutral measure Q , respectively. Using Merton's portfolio as a benchmark portfolio, the optimal terminal wealth of the Q -risk constraint problem can be easily replicated with the standard delta hedging strategy. Motivated by this, we consider the Q -strategy fulfilling the P -risk constraint and compare its solution with the true optimal solution of the P -risk constraint problem. We show the existence and uniqueness of the optimal solution to the Q -strategy fulfilling the P -risk constraint, and provide a tractable evaluation method. The Q -strategy fulfilling the P -risk constraint is not only easier to implement with standard forwards and puts on a benchmark portfolio than the P -risk constraint problem, but also easier to solve than either of the Q - or P -risk constraint problem. The numerical test shows that the difference of the values of the two strategies (the Q -strategy fulfilling the P -risk constraint and the optimal strategy solving the P -risk constraint problem) is reasonably small. [ABSTRACT FROM AUTHOR]

We investigate an optimal growth portfolio problem with contingent convertible bonds (CoCos). As the conversion risk in CoCos is closely associated with the issuer's capital structure and the stock price at conversion, we model both equity and credit risk to frame this optimisation problem. This study aims to answer two questions that (i) how investors should optimally allocate their financial wealth between a CoCo and a risk-free bond; and (ii) which approach – investing in a CoCo or in a stock issued by the same bank – could result in higher expected returns. First, we derive the dynamic of a coupon-paying CoCo price under a reduced-form approach. We then decompose the problem into pre- and post-conversion regimes to obtain closed-form optimal strategies. A comparative simulation leads us to conclude that, under various market conditions, investing in a CoCo with a risk-free bond provides a higher expected growth than investing in stock. [ABSTRACT FROM AUTHOR]

In this paper, we study a constrained utility maximization problem following the convex duality approach. After formulating the primal and dual problems, we construct the necessary and sufficient conditions for both the primal and dual problems in terms of forward and backward stochastic differential equations (FBSDEs) plus some additional conditions. Such formulation then allows us to explicitly characterize the primal optimal control as a function of the adjoint process coming from the dual FBSDEs in a dynamic fashion and vice versa. We also find that the optimal wealth process coincides with the adjoint process of the dual problem and vice versa. Finally we solve three constrained utility maximization problems, which contrasts the simplicity of the duality approach we propose and the technical complexity of solving the primal problem directly. [ABSTRACT FROM AUTHOR]

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. [ABSTRACT FROM AUTHOR]

In this paper, we propose a new algorithm to find the optimal static replicating portfolios for general path-independent nonlinear pay-off functions and give an estimate for the rate of convergence that is absent in the literature. We choose the static replication by designing an adaptation function arising in the error bound between the nonlinear pay-off function and the linear spline approximation and derive the equidistribution equation for selecting the optimal strikes. The numerical tests for variance swaps, swaptions, static quadratic hedges and also for a jump-diffusion process, allowing for the default of the underlying asset, show that the proposed iterative equidistribution equation algorithm is simple, fast and accurate. The paper generalizes and improves the results on static replication and approximation in the literature. [ABSTRACT FROM AUTHOR]

We maximize the expected utility of terminal wealth in an incomplete market where there are cone constraints on the investor's portfolio process and the utility function is not assumed to be strictly concave or differentiable. We establish the existence of the optimal solutions to the primal and dual problems and their dual relationship. We simplify the present proofs in this area and extend the existing duality theory to the constrained nonsmooth setting. [ABSTRACT FROM AUTHOR]

In this paper, we derive an easily computed approximation to European basket call prices for a local volatility jump-diffusion model. We apply the asymptotic expansion method to find the approximate value of the lower bound of European basket call prices. If the local volatility function is time independent then there is a closed-form expression for the approximation. Numerical tests show that the suggested approximation is fast and accurate in comparison with the Monte Carlo (MC) and other approximation methods in the literature. [ABSTRACT FROM AUTHOR]

The article discusses a study on pricing basket of credit default swaps. The authors proposed a simple method in computing ordered default time distributions in both the homogenous case and two-group heterogeneous case under intensity default contagion model. It explores the ordered default time in limiting case and includes the exponential decay and the multistate stochastic intensity process. The study outperforms Monte Carlo method with respect to the valuation of swap rates.

We propose a copula contagion mixture model for correlated default times. The model includes the well-known factor, copula, and contagion models as its special cases. The key advantage of such a model is that we can study the interaction of different models and their pricing impact. Specifically, we model the default times of the underlying names in a reference portfolio to follow contagion intensity processes with exponential decay coupled with a copula dependence structure. We also model the default time of the counterparty and its dependence structure with the reference portfolio. Numerical tests show that correlation and contagion have an enormous joint impact on the rates of CDO tranches and the corresponding credit value adjustments are extremely high to compensate for the wrong-way risk. [ABSTRACT FROM AUTHOR]

One of the central issues in credit risk measurement and management is modeling and predicting correlated defaults. In this paper we introduce a novel model to investigate the relationship between correlated defaults of different industrial sectors and business cycles as well as the impacts of business cycles on modeling and predicting correlated defaults using the Probabilistic Boolean Network (PBN). The key idea of the PBN is to decompose a transition probability matrix describing correlated defaults of different sectors into several BN matrices which contain information about business cycles. An efficient estimation method based on an entropy approach is used to estimate the model parameters. Using real default data, we build a PBN for explaining the default structure and making reasonably good predictions of joint defaults in different sectors. [ABSTRACT FROM AUTHOR]