Optimal regulation policies for a multipurpose reservoir with seasonal input and return function

Optimal regulation policies for a multipurpose reservoir are characterized analytically for the case where the input and return functions are subject to seasonal variations and the return function is piecewise linear, concave, and separable in reservoir volume and discharge. Efficient upper and lower bounds on optimal policies are derived for two important special cases. Necessary and sufficient conditions are obtained for a finite-time horizon optimal policy to be also optimal for the infinite-time horizon.This research was supported in part by the Office of Water Resources Research, Grant No. A-043-CAL, through the Water Resources Center, University of California.     

Optimal time-consistent investment and reinsurance policies for mean-variance insurers

This paper investigates the optimal time-consistent policies of an investment-reinsurance problem and an investment-only problem under the mean-variance criterion for an insurer whose surplus process is approximated by a Brownian motion with drift. The financial market considered by the insurer consists of one risk-free asset and multiple risky assets whose price processes follow geometric Brownian motions. A general verification theorem is developed, and explicit closed-form expressions of the optimal polices and the optimal value functions are derived for the two problems. Economic implications and numerical sensitivity analysis are presented for our results. Our main findings are: (i) the optimal time-consistent policies of both problems are independent of their corresponding wealth processes; (ii) the two problems have the same optimal investment policies; (iii) the parameters of the risky assets (the insurance market) have no impact on the optimal reinsurance (investment) policy; (iv) the premium return rate of the insurer does not affect the optimal policies but affects the optimal value functions; (v) reinsurance can increase the mean-variance utility.     

OPTIMAL MODELS FOR THE FIRST ARRIVAL TIME DISTRIBUTION FUNCTION IN CONTINUOUS TIME－WITH A SPECIAL CASE

ＯＰＴＩＭＡＬＭＯＤＥＬＳＦＯＲＴＨＥＦＩＲＳＴＡＲＲＩＶＡＬＴＩＭＥＤＩＳＴＲＩＢＵＴＩＯＮＦＵＮＣＴＩＯＮＩＮＣＯＮＴＩＮＵＯＵＳＴＩＭＥ－ＷＩＴＨＡＳＰＥＣＩＡＬＣＡＳＥＬＩＮＹＵＡＮＬＩＥ（林元烈）（ＤｅｐａｒｔｍｅｎｔｏｆＡｐｐｌｉｅｄＭａ...     

An optimal investment and consumption model with stochastic returns

We consider a financial market consisting of a risky asset and a riskless one, with a constant or random investment horizon. The interest rate from the riskless asset is constant, but the relative return rate from the risky asset is stochastic with an unknown parameter in its distribution. Following the Bayesian approach, the optimal investment and consumption problem is formulated as a Markov decision process. We incorporate the concept of risk aversion into the model and characterize the optimal strategies for both the power and logarithmic utility functions with a constant relative risk aversion (CRRA). Numerical examples are provided that support the intuition that a higher proportion of investment should be allocated to the risky asset if the mean return rate on the risky asset is higher or the risky asset return rate is less volatile. Copyright © 2008 John Wiley & Sons, Ltd.     

Optimal expansion and design of competence sets with asymmetric acquiring costs

This paper provides a method of finding the optimal expansion process and discusses the marginal analysis for expansion of the competence set when the cost functions are asymmetric. The concept of tree expansion process is introduced, and a method of finding the optimal tree expansion process is given. The paper also shows a way to identify the optimal competence set when both the expected return and cost are considered.     

Optimization of a Multiperiod Resource Allocation Model

In this paper we examine multiperiod resource allocation problems, such as allocating a given marketing budget among T periods. The return functions of each period are assumed to be concave functions of the effective effort variable, which is composed of the expenditures in all previous periods and the present one. Assuming that the effect of an amount spent in period t is decreasing by a fixed rate in successive periods, necessary and sufficient conditions for a non-boundary optimal policy are derived. Under these conditions the optimal policy which maximizes total returns is obtained.     

Oil Exploration: A Property of Beale's Model

In this paper we assume that an oil company has k areas in which to drill and occurrences of undiscovered oilfields are represented by the model of Beale. The company is seeking a strategy for drilling that maximizes its expected return under the constraint that the total amount spent on drilling in all areas must not exceed R. This leads to an integer programming problem. We establish that the expected return functions for the separate areas are concave and that this property can be used to reduce the computational effort required to find an optimal solution.     

考虑收益率及破产补偿函数的奇异最优随机控制模型

通过在目标结构中引入收益率及破产补偿函数,建立了一非对称型最优奇异随机控制模型.利用随机积分及最优控制理论,得出了最大回报函数的显式解及相应的最优控制策略.     

Piecewise affine approximations for the control of a one-reservoir hydroelectric system

We analyze the computation of optimal and approximately optimal policies for a discrete-time model of a single reservoir whose discharges generate hydroelectric power. Inflows in successive periods are random variables. Revenue from hydroelectric production is represented by a piecewise linear function. We use the special structure of optimal policies, together with piecewise affine approximations of the optimal return functions at each stage of dynamic programming, to decrease the computational effort by an order of magnitude compared with ordinary value iteration. The method is then used to obtain easily computable lower and upper bounds on the value function of an optimal policy, and a policy whose value function is between the bounds.     

Portfolios with fuzzy returns: Selection strategies based on semi-infinite programming

This paper provides new models for portfolio selection in which the returns on securities are considered fuzzy numbers rather than random variables. The investor's problem is to find the portfolio that minimizes the risk of achieving a return that is not less than the return of a riskless asset. The corresponding optimal portfolio is derived using semi-infinite programming in a soft framework. The return on each asset and their membership functions are described using historical data. The investment risk is approximated by mean intervals which evaluate the downside risk for a given fuzzy portfolio. This approach is illustrated with a numerical example.     

Discrete allocation of a linear resource according to a sum-of-products objective

The allocation of a linear resource according to the sum of the returns from independent activities is considered. The return from each activity is given by a product of concave and nondecreasing functions of a single allocation variable. The model can be used, for instance, to describe probabilities of success of several serial tasks, into which an activity is subdivided. An incremental algorithm is defined and conditions are given for the algorithm to generate an optimal solution; otherwise, the problem is solved by a two-step procedure involving the incremental maximization of the return corresponding to a single activity and the combination of the activities by dynamic programming. Examples are given of problems solvable and not solvable by the incremental algorithm.     

Location of a discrete resource and its allocation according to a fractional objective

The problem considered is that of the location of a discrete resource and its allocation to activities with concave return functions in such a way as to maximize the ratio of ‘return’ to ‘cost’, the total cost being the sum of a fixed cost and linearly variable costs. It is assumed that each resource has an effectiveness of 0 or 1 against each activity. It is demonstrated that an optimal solution can be determined by the rounding to integers of the solution of an associated problem in continuous variables. Solutions with objective values arbitrarily close to the optimal value can be generated by resource-wise optimizations. An upper bound of the number of non-zero integer allocations in an optimal solution is derived.     

Continuous time Markovian decision processes average return criterion

Continuous time Markovian decision models with countable state space are investigated. The existence of an optimal stationary policy is established for the expected average return criterion function. It is shown that the expected average return can be expressed as an expected discounted return of a related Markovian decision process. A policy iteration method is given which converges to an optimal deterministic policy, the policy so obtained is shown optimal over all Markov policies.     

Utility maximization with partial information: Hamilton-Jacobi-Bellman equation approach

This paper deals with the problem of maximizing the expected utility of the terminal wealth when the stock price satisfies a stochastic differential equation with instantaneous rates of return modelled as an Ornstein-Uhlenbeck process. Here, only the stock price and interest rate can be observable for an investor. It is reduced to a partially observed stochastic control problem. Combining the filtering theory with the dynamic programming approach, explicit representations of the optimal value functions and corresponding optimal strategies are derived. Moreover, closed-form solutions are provided in two cases of exponential utility and logarithmic utility. In particular, logarithmic utility is considered under the restriction of short-selling and borrowing.      

Ratio dynamic programs

This paper considers a finite serial multistage system where the measure of effectiveness of the system is a ratio of two return functions. The numerator of the ratio is an additive return function whereas the denominator is a multiplicative one. Because of the difference in the nature of the separability of the two factors, standard parametric approaches do not generate returns which are separable. Hence, the resulting formulation cannot be solved by dynamic programming. We consider an associated two-criteria dynamic program and show that the optimal solution is a nondominated solution of the two criteria program. An efficient search algorithm through the nondominated solutions is presented to solve this class of serial multistage decision systems. Computational results are presented to demonstrate the effectiveness of this approach.     

Discrete Allocation and Replenishment of Resources with Binary Effectiveness

The problem considered is that of the allocation and replenishment of several resources in integer quantities in such a way as to maximize the sum of the returns from activities with concave return functions. All the resources are of the same physical type and each resource has an effectiveness of 0 or 1 against each activity, depending on the geographical locations of the resources and the activities or on other constraints. Solutions with objective values arbitrarily close to the optimal value are generated by the application of resourcewise optimization to an associated problem in continuous variables, and the rounding of a continuous solution to an integer solution according to given rules. The application of other continuous methods is indicated. Some properties of optimal integer solutions are derived.     

Optimal periodic dividend and capital injection problem for spectrally positive Lévy processes

In this paper, we investigate an optimal periodic dividend and capital injection problem for spectrally positive Lévy processes. We assume that the periodic dividend strategy has exponential inter-dividend-decision times and continuous monitoring of solvency. Both proportional and fixed transaction costs from capital injection are considered. The objective is to maximize the total value of the expected discounted dividends and the penalized discounted capital injections until the time of ruin. By the fluctuation theory of Lévy processes in Albrecher et al. (2016), the optimal periodic dividend and capital injection strategies are derived. We also find that the optimal return function can be expressed in terms of the scale functions of Lévy processes. Finally, numerical examples are studied to illustrate our results.     

New concepts and algorithms for portfolio choice

The paper studies the design of optimal (bond) portfolios taking into account various possible utility functions of an investor. The most prominent model for portfolio optimization was introduced by Markowitz. A real solution in this model can be achieved by quadratic programming routines for mean-variance analysis. Of course, there are many reasons for an investor to prefer other utility criteria than return/variance of return in the Markowitz model. In the last few years, many efficient multiple purpose optimization heuristics have been invented for the needs in optimizing telephone nets, chip layouts, job shop scheduling etc. Some of these heuristics have essential advantages: they are extremely flexible and very easy to implement on computers. One example of such an algorithm is the threshold-accepting algorithm (TA). TA is able to optimize portfolios under nearby arbitrary constraints and subject to nearly every utility function. In particular, the utility functions need neither to be convex, differentiable nor ‘smooth’ in any sense. We implemented TA for bond portfolio optimization with different utility criteria. The algorithms and computational results are presented. Under various utility functions, the ‘best’ portfolios look surprisingly different and have quite different qualities. Thus, for a portfolio manager it might be useful to provide himself with such a ‘multiple-taste’ optimizer in order to be able easily to readjust it according to his own personal utility considerations.     

The optimal solution of ESG portfolio selection models that are based on the average ESG score

Recently, various models have been proposed to engage portfolio selection or ESG investments. In this brief report, we solve the problem of optimal portfolio selection of arbitrary ESG utility functions where the ESG preference function is based on the average ESG score. The proposed optimal solution shows that the impact of the ESG score and the expected return vectors on the optimal weights are equal, up to a scalar, regardless of the utility function of the investors.     

An integrated product returns model with logistics and marketing coordination

We develop an integrated approach for analyzing logistics and marketing decisions within the context of designing an optimal returns system for a retailer servicing two distinct market segments. At the operational level, we show that the optimal refund price is not unique. Moreover, it is such that if both market segments return a purchased product, then neither segment will receive a full money-back refund; and it is such that if one or both segments do not return a purchased product, then a refund premium over the purchase price is possible, but the refund premium will not be enough to offset a customer's total net cost of purchase and return. We also show that any improvement to the returns system that results in increased logistical efficiency or marketing effectiveness will be accompanied by an increase in the selling price of the product. At the strategic level, we show that if the retailer does not coordinate its logistics and marketing efforts to improve the overall returns system, then it will tend to over-invest in one of the functions and under-invest in the other. Finally, we illustrate how our model can be generalized to the case in which a customer's ex post valuation of the product falls along a continuum.