OPTIMAL INVESTMENT IN THE PROTECTION OF A VULNERABLE BIOLOGICAL RESOURCE

It is assumed that the probability of destruction of a biological asset by natural hazards can be reduced through investment in protection. Specifically a model, in which the hazard rate depends on both the age of the asset and the accumulated invested protection capital, is assumed. The protection capital depreciates through time and its effectiveness in reducing the hazard rate is subject to diminishing returns. It is shown how the investment schedule to maximize the expected net present value of the asset can be determined using the methods of deterministic optimal control, with the survival probability regarded as a state variable. The optimal investment pattern involves “bang-bang-singular” control. A numerical scheme for determining jointly the optimal investment policy and the optimal harvest (or replacement) age is outlined and a numerical example involving forest fire protection is given.     

Loss-based quality costs and inventory planning: General models and insights

In this paper, we examine a joint lot-sizing and process investment problem with random yield and backorders. We allow for inspection and develop stochastic models which provide the optimal inspection and lot-sizing policy as well as the optimal process investment for variance reduction. The process quality loss profile around the target is captured via a modification of the Reflected Normal loss function. We conduct numerical experiments assuming that the proportion of defectives follows a Uniform distribution while the process quality characteristic follows either a Normal or Uniform distribution. We also develop closed-form solutions that depend on at most the first two moments of any general probability distribution of defective units and which allow us to examine the nature of optimal policies. We demonstrate via numerical experiments the value of our integrated approach for jointly determining optimal inventory, inspection, and investment policies. Overall, our models and analyses provide some interesting insights into this reasonably complex inventory-quality problem and open up several avenues for future work in this area.     

Continuous time mean variance asset allocation: A time-consistent strategy

We develop a numerical scheme for determining the optimal asset allocation strategy for time-consistent, continuous time, mean variance optimization. Any type of constraint can be applied to the investment policy. The optimal policies for time-consistent and pre-commitment strategies are compared. When realistic constraints are applied, the efficient frontiers for the pre-commitment and time-consistent strategies are similar, but the optimal investment strategies are quite different.     

Liquidity risk and optimal dividend/investment strategies

In this paper, we study the problem of determining an optimal control on the dividend and investment policy of a firm operating under uncertain environment and risk constraints. We allow the company to make investment decisions by acquiring or selling producing assets whose value is governed by a stochastic process. The firm may face liquidity costs when it decides to buy or sell assets. We formulate this problem as a multi-dimensional mixed singular and multi-switching control problem and use a viscosity solution approach. We numerically compute our optimal strategies and enrich our studies with numerical results and illustrations.     

IRREVERSIBLE INVESTMENT AND OPTIMAL FOREST EXPLOITATION

A forest harvest scheduling model which includes as activities the level of investment in harvest capacity and the accumulated harvest capacity in each period, is presented. The inclusion of these activities, in addition to the harvest activities, allows for the removal of harvest-flow constraints found in more typical Model II formulations of the harvest scheduling problem. The optimal harvest and investment policy can be determined by linear programming or quadratic programming methods, depending on whether prices are constant or supply-dependent. The new model better reflects economic reality than existing models, and provides a method for determining the optimal economic development of a forest industry, and the optimal draw-down of old growth forest. Numerical examples are given.     

An Optimal Diversification Network Model with Fixed-Solution Universe Subsets

This paper develops a generalized dynamic network model for portfolio investment diversification. The model considers the situation of the fixed solution subset corresponding to a fixed single-resource economic investment such as that found in many oil-producing nations. Quadratic side constraints on the variance of the resultant flow distribution are added to the model to accommodate uncertainty. The model has been tested using a prototype example. The results indicate that the risk associated with a single-resource investment can be reduced by determining optimal investment weights.     

一类线性规划问题的快速解法

研究了在组合投资和多属性决策指标权重确定中有着重要应用的一类线性规划问题,得到了该类线性规划问题有可行解的充要条件,以及在有可行解的情况下寻求最优解的快速解法.     

Determination of the portfolio selection for a property-liability insurance company

This paper presents an analysis of a portfolio model which can be used to assist a property-liability insurance company in determining the optimal composition of the insurance and investment portfolios. By introducing insurer's threshold risk and relaxing some non-realistic assumptions made in traditional chance constraint insurance and investment portfolio models, we propose a method for an insurer to maximize his return threshold for a given threshold risk level. This proposed model can be used to optimize the composition of underwriting and investment portfolios regarding the insurer's threshold risk level, as well as to generate the efficient frontier by adjusting insurer's threshold risk levels. A numerical example is given based on the industry's aggregated data for a sixteen year period.     

A Higher-Order Hidden Markov Chain-Modulated Model for Asset Allocation

This paper presents an analysis of asset allocation strategies when the asset returns are governed by a discrete-time higher-order hidden Markov model (HOHMM), also called the weak hidden Markov model. We assume the drifts and volatilities of the asset returns switch over time according to the state of the HOHMM, in which the probability of the current state depends on the information from previous time-steps. The “switching” and “mixed” strategies are studied. We use a multivariate filtering technique in conjunction with the EM algorithm to obtain estimates of model parameter at a given time. This, in turn, aids investors in determining the optimal investment strategy for the next time step. Numerical implementation is applied to data on Russell 3000 value and growth indices. We benchmark the respective performances of portfolio using three classical investment measures.     

Stabilizing the Hamiltonian system for constructing optimal trajectories

An infinite-horizon optimal control problem based on an economic growth model is studied. The goal in the problem is to optimize the mechanisms of investment in basic production assets in order to increase the growth rate of the consumption level. The main output variable-the gross domestic product (GDP)-depends on three production factors: capital stock, human capital, and useful work. The first two factors are endogenous variables of the model, and the useful work is an exogenous factor. The dependence of the GDP on the production factors is described by the Cobb-Douglas power-type production function. The economic system under consideration is assumed to be closed, so the GDP is distributed between consumption and investment in the capital stock and human capital. The optimal control problem consists in determining optimal investment strategies that maximize the integral discounted relative consumption index on an infinite time interval. A solution to the problem is constructed on the basis of the Pontryagin maximum principle adapted to infinite-horizon problems. We examine the questions of existence and uniqueness of a solution, verify necessary and sufficient optimality conditions, and perform a qualitative analysis of Hamiltonian systems on the basis of which we propose an algorithm for constructing optimal trajectories. This algorithm uses information on solutions obtained by means of a nonlinear regulator. Finally, we estimate the accuracy of the algorithm with respect to the integral cost functional of the control process.     

Managerial and economic impacts of reducing delivery variance in the supply chain

This paper addresses the managerial and economic impacts of improving delivery performance in a serial supply chain when delivery performance is evaluated with respect to a delivery window. Building on contemporary management theories that advocate variance reduction as the critical step in improving the overall performance of a system, we model the variance of delivery time to the final customer as a function of the investment to reduce delivery variance and the costs associated with untimely delivery (expected earliness and lateness). A logarithmic investment function is used and the model solution involves the minimization of a convex–concave total cost function. A numerical example is provided to illustrate the model and the solution procedure. The model presented provides guidelines for determining the optimal level of financial investment for reducing delivery variance. The managerial implications as well as the economic aspects of delivery variance reduction in supply chain management are discussed.     

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This paper considers a dividend strategy with investment in Omega model. If at a potential dividend-payment time the surplus is above, part of the excess are paid as dividends directly, the other part are used as dynamic investment capital, at a particular time, the sum of profits and investment capital will be paid as another dividend. Under this dividend policy, we get the optimal dividend strategy and the optimal portfolio policy.     

Analysis of the expected discounted penalty function for a general jump-diffusion risk model and applications in finance

In this paper, we extend the Cramér-Lundberg risk model perturbed by diffusion to incorporate the jumps of surplus investment return. Under the assumption that the jump of surplus investment return follows a compound Poisson process with Laplace distributed jump sizes, we obtain the explicit closed-form expression of the resulting Gerber-Shiu expected discounted penalty (EDP) function through the Wiener-Hopf factorization technique instead of the integro-differential equation approach. Especially, when the claim distribution is of Phase-type, the expression of the EDP function is simplified even further as a compact matrix-type form. Finally, the financial applications include pricing barrier option and perpetual American put option and determining the optimal capital structure of a firm with endogenous default.     

Optimal input substitution of a firm facing an environmental constraint

In this paper we consider the dynamic behavior of a firm subject to environmental regulation. As a social planner the government wants to reduce the level of pollution. To reach that aim it can, among others, set an upper limit on polluting emissions of the firm. The paper determines how this policy instrument influences the firm's decisions concerning investments, abatement efforts, and the choice whether to leave some capacity unused or not. The abatement process is modeled as input substitution rather than end-of-pipe. Using standard control theory in determining the firm's optimal dynamic investment decisions it turns out that it is always optimal to approach a long run optimal level of capital. In some cases, this equilibrium is reached within finite time, but usually it will be approached asymptotically. Different scenarios are considered, ranging from attractive clean input to unattractive clean input, and from a mild emission limit to a very tight one. It is shown that for large capital stocks and/or when marginal cash flow per unit of emissions is larger for the dirty input than for the clean input, it can be optimal to actually leave some production capacity unused. Also, since the convex installation costs suggest to spread investments over time, it can happen that investment in productive capital is positive although capacity remains unused.     

Determining the optimal number of depots in a physical distribution system according to market characteristics

This paper is an extension of an earlier paper to investigate the interactive effects of location, price and demand using mathematical models of distribution systems.The paper considers the additive nature of solutions to depot location problems and shows how this property can be used to advantage in determining the optimal number of depots in a distribution system. The importance of using marginal profit and marginal return on investment in this context is demonstrated.The sensitivity of the results to changes in cost parameters is also discussed.     

随机市场中均值-方差模型最优投资策略的时间不相容性及其修正

由于方差算子在动态规划意义下不可分,导致随机市场中多期均值一方差模型的最优投资策略不满足时间相容性,即Bellman最优性原理．为此,首先提出了随机市场中比Bellman最优性原理更弱的时间相容性,并证明在投资区间的任意中间时刻,当投资者的财富不超过某一给定的财富阈值时,最优投资策略满足弱时间相容性;当投资者的财富超过该阈值时,最优投资策略将不再是弱时间相容的,且导致投资者变为非理性,即他会同时极小化终期财富的均值和方差．在这种情形下,通过放松自融资约束,对最优投资策略进行了修正,使得其满足：修正策略可使投资者回归理性;相对于终期财富,修正策略可以获得与最优投资策略相同的均值和方差．在策略修正过程中,投资者可以从市场中获得一个严格正的现金流．这些结果表明修正策略要优于原最优投资策略,拓展了现有关于确定市场下多期均值．方差模型的求解以及策略时间相容性的结论．     

Investment in electricity networks with transmission switching

We consider the application of Dantzig-Wolfe decomposition to stochastic integer programming problems arising in the capacity planning of electricity transmission networks that have some switchable transmission elements. The decomposition enables a column-generation algorithm to be applied, which allows the solution of large problem instances. The methodology is illustrated by its application to a problem of determining the optimal investment in switching equipment and transmission capacity for an existing network. Computational tests on IEEE test networks with 73 nodes and 118 nodes confirm the efficiency of the approach.     

随机利率及随机收益保证下的投资策略

考虑随机利率环境及随机收益保证下基金经理的投资组合问题。利用鞅方法,得到了最优投资策略的显性解。结论表明,最优投资策略包括三个部分：投机策略、利率套期保值策略以及随机收益保证的复制策略,且该最优策略等价于将一部分资金投资于确保终端时刻获得最低收益的基准组合,而剩余资金则依照无保证情况下的最优策略进行投资。     

Optimal investment in a defaultable bond

The present paper analyzes the optimal investment strategy in a defaultable (corporate) bond and a money market account in a continuous time model. Due to jumps in the bond price our market model is incomplete. The treatment of information on the firm’s asset value is based on an approach unifying the structural model and the reduced-form model. Specifically, the asset value will be assumed to be observable only at finitely many time points before the maturity of the bond. The optimal investment process will be worked out first for a short time-horizon with a general risk-averse utility function, then a multi-period optimal strategy with logarithmic and power utility will be presented using backward induction. The optimal investment strategy is analyzed numerically for the logarithmic utility.