A polyhedral approximation approach to concave numerical dynamic programming

This paper introduces a numerical method for solving concave continuous state dynamic programming problems which is based on a pair of polyhedral approximations of concave functions. The method is globally convergent and produces computable upper and lower bounds on the value function which can in theory be made arbitrarily tight. This is true regardless of the pattern of binding constraints, the smoothness of model primitives, and the dimensionality and rectangularity of the state space. We illustrate the method's performance using an optimal firm management problem subject to credit constraints and partial investment irreversibilities.     

网上新股申购中的资金规划研究

网上新股申购通常被认为是风险较低而收益稳定的投资策略。由于新股投资机会较为密集且短期占用资金较多,面对多个申购机会的合理取舍及资金的高效使用将显得尤为重要。通过将新股申购问题抽象为一般连续投资下的资金规划问题,给出其约束方程,指出其求解方法,然后讨论了新股申购在两种目标下的资金规划,并与未做资金规划的简单方案进行比较,结果显示该方法有效地达到了规划目标,提高了整体收益。     

Manpower targets and educational investments

Quadratic programming can be useful to compute the optimal investment trajectory for an education system which is planned on the base of manpower targets. The computation of optimal investments required to approach manpower targets more closely becomes non trivial if the budget available is insufficient to meet manpower targets exactly, or if the manpower target trajectory is erratic.The quadratic programming problem consists of three components: (1) an optimization criterion which reflects the objective to minimize the squared deviation of actual manpower available from the manpower target; (2) a set of time difference equations which reflect the flow of students, the manpower stock flow and the flow of investments in the education subsystem; (3) a constraint on the budget, available for this branch of education over a planning period.This education investment problem is worked out for middle level technical manpower training in Bangladesh.     

Incomplete markets, ambiguity, and irreversible investment

The problem of irreversible investment with idiosyncratic risk is studied by interpreting market incompleteness as a source of ambiguity over the appropriate no-arbitrage discount factor. The maxmin utility over multiple priors framework is used to model and solve the irreversible investment problem. Multiple priors are modeled using the notion of κ‐ignorance. This set-up is used to analyze finitely lived options. For infinitely lived options the notion of constant κ‐ignorance is introduced. For these sets of density generators the corresponding optimal stopping problem is solved for general (in-)finite horizon optimal stopping problems driven by geometric Brownian motion. It is argued that an increase in the set of priors delays investment, whereas an increase in the degree of market completeness can have a non-monotonic effect on investment.     

Option Contracts in Supply Chains

This paper considers optimal contracts in supply chains that consist of   n ≥ 2  firms and face a potential investment hold-up problem. We show that option contracts may solve the incentive problems. First, we provide case-study evidence for the use of option contracts in the semiconductor industry. As our second contribution, we generalize the earlier option contract approach by introducing continuous quantities. Third, we extend the setting to n parties. For long supply chains, the first-best allocation can be achieved if there is a particular order of renegotiations .     

Structural change and technological development

It is important for our understanding of sectoral and regional structural change to analyze the R & D-activities. In this paper we show that R & D should be analyzed as an endogenous, intermediate, public investment variable rather than as ordinary capital investment. The allocation of resources for R&D cannot be decentralized regionally or sectorally but should preferably be decided on as a problem of optimal taxation. It is shown that the optimal rate of taxation for R&D is determined by possibilities of substitution between ordinary capital investments and R&D, by the propensity to invest and by the productivity of the R&D- producing sector. A dynamic model with accessibility representation of knowledge is finally formulated. This interregional R&D-model also has equilibrium growth properties. The equilibrium rate of growth of all regions of this model can be raised by decreasing any interregional distance or by raising any regional propensity to invest.     

An investment planning model for the electricity sector in Nigeria

In this study the methodology of mixed integer programming is used to deal with investment resource allocation problems that involve economies of scale in the Nigerial economic planning environment. The specific application is to long-term investment decisions in the government-operated electric power supply industry (NEPA). The investment planning problem involves determining the optimal generating plant/transmission mix from among a set of fossil fuel and conventional hydro plants which will meet the demand for electricity in Nigeria over the next three decades at minimum cost. Economies of scale in plant construction makes the investment cost function to be non-linear. However the non-linearity is approximated by a fixed charge function. Alternative price assumptions are made about locally found fuel resources (oil, gas, coal and liguite) to calculate the energy cost of fossil fuel plants. Different investment strategies are then evaluated in terms of the present values of the cost of supplying electricity to meet the required demand.     

An analytical solution for the robust investment-reinsurance strategy with general utilities

In financial markets, different investors have different attitudes or preferences on the investment policies and reinsurance problems. For investors with different investment utilities, how to provide an optimal investment strategy is not only a very hard problem, but also an urgent problem to be solved. In this paper, we derive an analytical solution for the optimal allocation problem of investment-reinsurance with general-form utility function. The general utility function allows for varying relative risk aversion coefficient, which is an important feature in finance theory. However, obtaining analytical solutions for general utility function has been difficult or impossible. The solution presented in this paper is constructed through the homotopy analysis method (HAM) and written in the form of a Taylor series expansion. The fully nonlinear Hamilton–Jacobi–Bellman (HJB) equation is decomposed into an infinite series of linear PDEs, which can be solved analytically. In the end, three examples are presented to illustrate the convergence and accuracy of the method, it also demonstrates that different risk reference investors have different investment-reinsurance strategies.     

Optimal investment models with vintage capital: Dynamic programming approach

The dynamic programming approach for a family of optimal investment models with vintage capital is here developed. The problem falls into the class of infinite horizon optimal control problems of PDE’s with age structure that have been studied in various papers (12, 11, 33 and 35) either in cases when explicit solutions can be found or using Maximum Principle techniques.     

Optimal investment and reinsurance policies for an insurer with ambiguity aversion

In this paper, we study the optimal investment and reinsurance problem for an insurer based on the variance premium principle, in which three cases are considered. First, we assume that the financial market does not exist. The insurer only holds an insurance business, and the optimal reinsurance problem is studied. Subsequently, we assume that there exists a financial market with an accurately modeled risky asset. The optimal investment and reinsurance problem is investigated under these conditions. Finally, we consider the general case in which the insurer is concerned about the model ambiguity of both the insurance market and the financial market. In all three cases, the value function is set to maximize the expected utility of terminal wealth. By employing the dynamic programming principle, we derive the Hamilton–Jacobi–Bellman (HJB) equations, which are satisfied by the value functions and obtain closed-form solutions for optimal reinsurance and investment policies and the value functions in all three cases. Most interestingly, we elucidate how investment improves the insurer’s utility and find that the existence of ambiguity can significantly affect the optimal policies and value functions. We also compare the ambiguities in the two markets and find that ambiguity in the insurance market has much more significant impact on the value function than the ambiguity in the financial market. It implies that it is more valuable for insurer to precisely evaluate the insurance risk. We also provide some numerical examples and economic explanations to illustrate our results.     

内部收益保证下养老基金的最优资产配置

研究内部收益保证下DC型养老基金的最优资产配置问题。利用鞅方法，在HJM利率期限结构下求得了最优资产配置的显性解。结论表明最优投资策略分为四部分：投机策略、利率套期保值策略、基准组合的复制策略及一揽予债券卖空策略。最后对最优策略的动态行为进行了数值分析。     

Investment planning for irrigation development projects

This paper considers the problem of choosing among the technologies available for irrigation by tubewells to obtain an investment plan which maximizes the net agricultural benefits from a proposed project in a developing country. Cost and benefit relationships are derived and incorporated into a mathematical model which is solved using a modification of the dynamic programming procedure for solving the knapsack problem. The optimal schedule is seen to favor small capacity wells, drilled by indigenous methods, with supplementary water distribution systems.     

Supplier evaluation and demand allocation among suppliers in a supply chain

This paper presents a hybrid algorithm that prioritizes the suppliers and then allocates the demand among the suppliers. The objective here is to maximize the total purchase value of the items taking into consideration budget constraint, demand condition, delivery lead-time and supplier capacity. Since the problem is multi-criteria decision making, we solve this problem by integrating the supplier rating with mixed linear integer programming method. The customer demand is allocated by using a hybrid algorithm based on the technique for order preference by similarity to ideal solution (TOPSIS) and the mixed linear integer programming (MILP) approaches. The effectiveness of the proposed algorithm is validated with computational results. Drawing to a case, a supplier S₃ is identified as the best supplier by using the TOPSIS method for demand allocation under no restrictions. On the contrary, under constrained scenario, supplier S₂ is selected as the best supplier by using the hybrid algorithm for demand allocation and maximum units are allocated to S₂.     

Privatization of businesses and flexible investment: a real option approach

In this article, we study the situation, where the opportunity is given to invest into a government-owned business by partial privatization to a private company. After payment of an initial installment cost, the private company’s investments are flexible within a range [0, k] until the business is completed. We model the problem in a real option framework, using geometric mean reversion to describe the dynamics of the business. We determine the optimal time for the private company to enter and pay the initial installment cost as well as the optimal dynamic investment strategy that it follows afterward. For the latter, analytic solution cannot be obtained. We use quadratic splines in order to solve the corresponding dynamic programming problem. Finally, we determine the optimal degree of privatization in our model from the government’s perspective.     

Hölder continuity of the policy function approximation in the value function approximation

We show that given a value function approximation V of a strongly concave stochastic dynamic programming problem (SDDP), the associated policy function approximation is Hölder continuous in V.     

投资收益不确定、投资期限与资产配置的动态调整策略

结合退休计划问题,本文在考虑了投资收益的不确定性后,在概率约束的框架下重新考察了不同投资期限下的最优资产配置问题,将传统的退休目标表示方法如"70@65"拓展为"70%的70@65",得出了不同投资期限下的最优资产配置策略。我们的研究表明,投资者越年轻则应持有更多的风险资产,并且,我们给出了随着年龄的增长,对资产配置进行的动态调整的可操作的具体路径,在理论上和实践上,特别是退休计划上具有一定的意义和运用价值。     

Adaptive algorithms for maximizing overall stock return

Deciding which stocks to purchase and how to optimally allocate the total investment among them is a nontrivial task for every investor. In this article, we propose two adaptive techniques that would provide an optimal allocation maximizing the return over the investment period. The first approach is the adaptive power method (PM) which is a modification of the proper orthogonal decomposition method. The adaptive PM uses only the currently available information to compute the optimal allocations, yet its long-term solution approaches the dominant eigen solution, even though that solution would require having a priori knowledge of all stocks’ performance. The second approach is derived from the well-known Least Mean Square (LMS) method, where the optimal allocation can be computed by adaptively steering the overall return toward a desired value. The experimental results have indicated promising gains even when the general market trend is downward.     

Strategic real options under asymmetric information

This paper studies the effect of private information on the capital allocation decisions of firms who operate under imperfect competition. I analyze two interactive firms, one with private information and the other without, who must decide when to undertake an irreversible and uncertain investment decision. Traditional non-strategic models of irreversible investment under uncertainty involve a single decision maker and result in an optimal period of delay before the investment is undertaken. In a strategic setting, firms must balance their desire to delay against competitive advantages from early investment. I find that an equilibrium may not exist within the standard continuous framework when the private information is over revenues. Moreover, when an equilibrium does exist the competitive pressures from the uninformed firm are weak. This is in contrast to existing models with asymmetric information over costs, where an equilibrium always exists and the competitive pressures remain strong (Hsu and Lambrecht, 2007). This work shows that the investment timing decision, and thus the value of the private information, is highly sensitive to the nature of incomplete information.     

油气配产问题的多目标规划模型及实证研究

在进行油气配产时,为了得到最优的配产计划,决策者往往需要考虑多个因素、多个目标,然而这些目标有的是不协调的,甚至是相互矛盾的。笔者根据石油企业油气配产的实际,提出了运用多目标规划的方法来解决该问题,建立了总资金投入量最小、总采油成本最低、总产量最大以及总利润最大的"多位一体"的多目标规划模型,并以D油田为例进行了实证研究,据此制订了该油田2010年的多目标配产方案,并与该油田实际的配产方案进行了对比,结果验证了模型的有效性,并指出了下一步研究的方向。     

Eliciting the socially optimal allocation from responsible agents

We consider designing a mechanism to allocate objects among agents without monetary transfers. There is a socially optimal allocation, which is commonly known by the agents but not observable by the designer. The designer possibly has information about the existence of responsible agents. A responsible agent, when indifferent between his objects at two different allocations, prefers the first allocation to the second if the first allocation is closer to the optimal allocation than the second, in the sense that all the agents who are allocated their optimal objects in the second allocation are allocated their optimal objects also in the first allocation, and there is at least one more agent in the first allocation receiving his optimal object. We show that, if the designer knows that there are at least three responsible agents, even if the identities of the responsible agents are not known, the optimal allocation can be elicited.