Induced effects and technological innovation with strategic environmental policy

This paper investigates an environmental policy designed to reduce the emission of pollutants under uncertainty, where the agents’ problem is formulated as an optimal stopping problem. We first analyze the single-agent’s case according to Pindyck [Pindyck, R.S., 2002. Optimal timing problems in environmental economics. Journal of Economic Dynamics and Control 26, 1677–1697]. We then extend the model to the case in which there are two competing agents. Therefore, we consider the external economic effects that are peculiar to an agent’s environmental policy decision. Finally, we consider the effect of technological innovation. The results of the analysis suggest that if there are two competing agents, they implement environmental policy simultaneously. Furthermore, the threshold for implementing environmental policy is higher when there are two agents, and how long these two agents take to implement environmental policy depends on the magnitude of the external economic effect. Furthermore, when we consider the effect of technological innovation, we show that the incentive to be the leader occurs if an additional condition is satisfied.     

Optimal cash management under uncertainty

We solve an agent’s optimization problem of meeting demands for cash over time with cash deposited in bank or invested in stock. The stock pays dividends and uncertain capital gains, and a commission is incurred in buying and selling of stock. We use a stochastic maximum principle to obtain explicitly the optimal transaction policy.     

Optimal investment, consumption and retirement choice problem with disutility and subsistence consumption constraints

In this paper we consider a general optimal consumption-portfolio selection problem of an infinitely-lived agent whose consumption rate process is subject to subsistence constraints before retirement. That is, her consumption rate should be greater than or equal to some positive constant before retirement. We integrate three optimal decisions which are the optimal consumption, the optimal investment choice and the optimal stopping problem in which the agent chooses her retirement time in one model. We obtain the explicit forms of optimal policies using a martingale method and a variational inequality arising from the dual function of the optimal stopping problem. We treat the optimal retirement time as the first hitting time when her wealth exceeds a certain wealth level which will be determined by a free boundary value problem and duality approaches. We also derive closed forms of the optimal wealth processes before and after retirement. Some numerical examples are presented for the case of constant relative risk aversion (CRRA) utility class.     

Optimal insurance under the insurer’s risk constraint

In this paper, we impose the insurer’s risk constraint on Arrow’s optimal insurance model. The insured aims to maximize his/her expected utility of terminal wealth, under the constraint that the insurer wishes to control the expected loss of his/her terminal wealth below some prespecified level. We solve the problem, and it is shown that when the insurer’s risk constraint is binding, the solution to the problem is not linear, but piecewise linear deductible. Moreover, it can be shown that the insured’s optimal expected utility will increase if the insurer increases his/her risk tolerance.     

Optimal portfolio, consumption and retirement decision under a preference change

We investigate an optimal portfolio, consumption and retirement decision problem in which an economic agent can determine the discretionary stopping time as a retirement time with constant labor wage and disutility. We allow the preference of the agent to be changed before and after retirement. It is assumed that the agent's coefficient of relative risk aversion becomes higher after retirement. Under a constant relative risk aversion (CRRA) utility function, we obtain the optimal policies in closed-forms using martingale methods and variational inequality methods. We give some numerical results of the optimal policies. We also consider the relation between the level of disutility and the labor wage with the optimal retirement wealth level.     

An optimal job,consumption/leisure,and investment policy

In this paper we investigate an optimal job, consumption, and investment policy of an economic agent in a continuous and infinite time horizon. The agent’s preference is characterized by the Cobb–Douglas utility function whose arguments are consumption and leisure. We use the martingale method to obtain the closed-form solution for the optimal job, consumption, and portfolio policy. We compare the optimal consumption and investment policy with that in the absence of job choice opportunities.     

Optimal consumption-leisure, portfolio and retirement selection based on α-maxmin expected CES utility with ambiguity

This article studies optimal consumption-leisure, portfolio and retirement selection of an infinitely lived investor whose preference is formulated by ??-maxmin expected CES utility which is to differentiate ambiguity and ambiguity attitude. Adopting the recursive multiplepriors utility and the technique of backward stochastic differential equations (BSDEs), we transform the ??-maxmin expected CES utility into a classical expected CES utility under a new probability measure related to the degree of an investor??s uncertainty. Our model investigates the optimal consumption-leisure-work selection, the optimal portfolio selection, and the optimal stopping problem. In this model, the investor is able to adjust her supply of labor flexibly above a certain minimum work-hour along with a retirement option. The problem can be analytically solved by using a variational inequality. And the optimal retirement time is given as the first time when her wealth exceeds a certain critical level. The optimal consumption-leisure and portfolio strategies before and after retirement are provided in closed forms. Finally, the distinctions of optimal consumption-leisure, portfolio and critical wealth level under ambiguity from those with no vagueness are discussed.     

Continuous-time mean–variance portfolio selection with liability and regime switching

A continuous-time mean–variance model for individual investors with stochastic liability in a Markovian regime switching financial market, is investigated as a generalization of the model of Zhou and Yin [Zhou, X.Y., Yin, G., 2003. Markowitz’s mean–variance portfolio selection with regime switching: A continuous-time model, SIAM J. Control Optim. 42 (4), 1466–1482]. We assume that the risky stock’s price is governed by a Markovian regime-switching geometric Brownian motion, and the liability follows a Markovian regime-switching Brownian motion with drift, respectively. The evolution of appreciation rates, volatility rates and the interest rates are modulated by the Markov chain, and the Markov switching diffusion is assumed to be independent of the underlying Brownian motion. The correlation between the risky asset and the liability is considered. The objective is to minimize the risk (measured by variance) of the terminal wealth subject to a given expected terminal wealth level. Using the Lagrange multiplier technique and the linear-quadratic control technique, we get the expressions of the optimal portfolio and the mean–variance efficient frontier in closed forms. Further, the results of our special case without liability is consistent with those results of Zhou and Yin [Zhou, X.Y., Yin, G., 2003. Markowitz’s mean–variance portfolio selection with regime switching: A continuous-time model, SIAM J. Control Optim. 42 (4), 1466–1482].     

Background risk,bivariate risk attitudes,and optimal prevention

This paper extends Eeckhoudt et al.’s (2012) results for precautionary effort to bivariate utility function framework. We establish an equivalence between the agent’s precautionary effort motive and the signs of successive cross-derivatives of the bivariate utility function. We show that the introduction (or deterioration) of an independent background risk induces more prevention to protect against wealth loss provided the individual exhibits correlation aversion of some given order. The conditions on the individual’s risk preferences are given to generate some specific prevention behaviors in the univariate framework with multiplicative risks. Our conclusion also indicates that an increase in the correlation between wealth risk and background risk leads to a reduction in optimal prevention.     

On the structure of the optimal server control for fluid networks

This paper derives the optimal trajectories in a general fluid network with server control. The stationary optimal policy in the complete state space is constructed. The optimal policy is constant on polyhedral convex cones. An algorithm is derived that computes these cones and the optimal policy. Generalized Klimov indices are introduced, they are used for characterizing myopic and time-uniformly optimal policies.Received: November 2004 / Revised: February 2005The research of this author has been supported by the project ‘‘Stochastic Networks’’ of the Netherlands Organisation for Scientific Research NWO.     

A dynamic model for optimal design quality and return policies

A clearly explained and generous return policy has been established as a competitive weapon to enhance sales. From the firm’s point of view, a generous return policy will increase sales revenue, but will also increase cost due to increased likelihood of return. Design quality of the product has been used as a competitive weapon for a long time. This paper recognizes the relationship between design quality and price of the product, and the firm’s return policy. Quality level in the product would influence the amount of return directly. When the product quality is higher, the customer satisfaction rate will increase and the probability of return will decrease. We develop a profit-maximization model to jointly obtain optimal policies for the product quality level, price and the return policy over time. The model presented in this paper is dynamic in nature and considers the decisions as the product moves through the life cycle. We obtain a number of managerial guidelines for using marketing and operational strategy variables to obtain the maximum benefit from the market. We mention several future research possibilities.     

Optimal compensation with adverse selection and dynamic actions

We consider continuous-time models in which the agent is paid at the end of the time horizon by the principal, who does not know the agent’s type. The agent dynamically affects either the drift of the underlying output process, or its volatility. The principal’s problem reduces to a calculus of variation problem for the agent’s level of utility. The optimal ratio of marginal utilities is random, via dependence on the underlying output process. When the agent affects the drift only, in the risk- neutral case lower volatility corresponds to the more incentive optimal contract for the smaller range of agents who get rent above the reservation utility. If only the volatility is affected, the optimal contract is necessarily non-incentive, unlike in the first-best case. We also suggest a procedure for finding simple and reasonable contracts, which, however, are not necessarily optimal. Research supported in part by NSF grants DMS 04-03575 and 06-31298. We would like to express our gratitude to participants of the following seminars and conferences for useful comments and suggestions: UCLA (Econ Theory), Caltech (Econ Theory), Columbia (Probability), Princeton (Fin. Engineering), U. Texas at Austin (Math Finance), Banff Workshop on Optim. Problems in Fin. Econ, Kyoto U. (Economics), UC Irvine (Probability), Cornell (Fin. Engineering), Bachelier Seminar. Moreover, we are very grateful to the anonymous referee for helpful suggestions. The remaining errors are the authors’ sole responsibility.     

Optimal Timing to Initiate Medical Treatment for a Disease Evolving as a Semi-Markov Process

In this paper, we consider the problem of the optimal timing to initiate a medical treatment. In the absence of treatment, we model the disease evolution as a semi-Markov process. The optimal time to initiate the treatment is a stopping time, which maximizes the total expected reward for the patient. We propose a stochastic dynamic programming formulation to find this stopping time. Under some plausible conditions, we show that the maximum total expected reward at the start of a health state will be smaller when the patient is in a more severe state. We then prove that the optimal policy for initializing the treatment is determined by a time threshold for each given health state. That is, in each health state, the treatment should be planned to start, when the patient’s duration time in the health state reaches (or exceeds, in the case of a late observation of the patient’s health status) a certain threshold level. We also present numerical examples to illustrate our model and to provide managerial insights.     

Consumption-Investment Problem with Subsistence Consumption,Bankruptcy, and Random Market Coefficients

We consider a general continuous-time finite-horizon single-agent consumption and portfolio decision problem with subsistence consumption and value of bankruptcy. Our analysis allows for random market coefficients and general continuously differentiable concave utility functions. We study the time of bankruptcy as a problem of optimal stopping, and succeed in obtaining explicit formulas for the optimal consumption and wealth processes in terms of the optimal bankruptcy time. This paper extends the results of Karatzas, Lehoczky, and Shreve (Ref. 1) on the maximization of expected utility from consumption in a financial market with random coefficients by incorporating subsistence consumption and bankruptcy. It also addresses the random coefficients and finite-horizon version of the problem treated by Sethi, Taksar, and Presman (Ref. 2). The mathematical tools used in our analysis are optimal stopping, stochastic control, martingale theory, and Girsanov change of measure.