Compromise programming with Tchebycheff norm for discrete stochastic orders

This paper presents a method of decision making with returns in the form of discrete random variables. The proposed method is based on two approaches: stochastic orders and compromise programming used in multi-objective programming. Stochastic orders are represented by stochastic dominance and inverse stochastic dominance. Compromise programming uses the augmented Tchebycheff norm. This norm, in special cases, takes form of the Kantorovich and Kolmogorov probability metrics. Moreover, in the paper we show applications of the presented methodology in the following problems: projects selections, decision tree and choosing a lottery.     

Newton-type methods for stochastic programming

Stochastic programming is concerned with practical procedures for decision making under uncertainty, by modelling uncertainties and risks associated with decision in a form suitable for optimization. The field is developing rapidly with contributions from many disciplines such as operations research, probability and statistics, and economics. A stochastic linear program with recourse can equivalently be formulated as a convex programming problem. The problem is often large-scale as the objective function involves an expectation, either over a discrete set of scenarios or as a multi-dimensional integral. Moreover, the objective function is possibly nondifferentiable. This paper provides a brief overview of recent developments on smooth approximation techniques and Newton-type methods for solving two-stage stochastic linear programs with recourse, and parallel implementation of these methods. A simple numerical example is used to signal the potential of smoothing approaches.     

Real options valuation of forest plantation investments in Brazil

In this paper, we consider investments in eucalyptus plantations in Brazil. For such projects, we discuss real options valuation in the place conventional methods such as IRR or NPV, possibly with CAPM. Traditionally, real options valuation assumes complete markets and neglects market imperfections. Yet, market frictions, such as transaction costs, interest rate spreads, and restricted short positions, can play an important role. We extend real options valuation to allow incomplete and imperfect markets. The value is obtained as a competitive price, given markets of competing investment opportunities, such as real and financial assets. Under perfect and complete markets, such valuation method is consistent with conventional real options theory. Stochastic programming and standard software is used for valuation of eucalyptus plantations. We estimate the underlying interdependent diffusion processes of stock market, interest rates, exchange rates and pulpwood price, and derive novel expressions of stochastic integrals to be employed in scenario generation for discrete time stochastic programming.     

非常规油气资源开发投资决策优化模型研究

非常规油气资源作为最现实的可替代能源,对其进行勘探和开发对于降低日益加大的石油供需矛盾缺口和确保国家能源安全均具有重要的战略意义。然而,非常规油气资源勘探开发十分复杂,开发投资决策好坏已经成为制约其能否实现规模化和产业化的关键问题,科学投资决策问题已逐步成为石油企业高层管理者的主要职责。针对非常规油气资源开发投资的多阶段多目标决策优化难题,以可供开发区块的资源分配为重点研究对象,从解决不同区块投资规模入手,运用多阶段决策、多目标决策和不确定多属性方案优选的方法理论,通过剖析非常规油气开发投资决策过程及其复杂性特征,将开发投资决策过程进行形式化描述并在计算机中加以实现,从而得以实现开发投资决策方案的动态性调整。本项研究不仅有助于深化多目标动态优化决策理论的研究,还为解决非常规油气资源开发投资决策难题提供一种新的思路和方法。     

Decision Analysis and Real Options: A Discrete Time Approach to Real Option Valuation

In this paper we seek to enhance the real options methodology developed by Copeland and Antikarov (2001) with traditional decision analysis tools to propose a discrete time method that allows the problem to be specified and solved with off the shelf decision analysis software. This method uses dynamic programming with an innovative algorithm to model the project’s stochastic process and real options with decision trees. The method is computationally intense, but simpler and more intuitive than traditional methods, thus allowing for greater flexibility in the modeling of the problem.     

Solving multistage asset investment problems by the sample average approximation method

The vast size of real world stochastic programming instances requires sampling to make them practically solvable. In this paper we extend the understanding of how sampling affects the solution quality of multistage stochastic programming problems. We present a new heuristic for determining good feasible solutions for a multistage decision problem. For power and log-utility functions we address the question of how tree structures, number of stages, number of outcomes and number of assets affect the solution quality. We also present a new method for evaluating the quality of first stage decisions.     

在未来收益不确定下的期权定价模型

§ 1　 IntroductionAt present,some high-technology(high-tech) firms such as information,software,pharmaceutical et al,are rapidly growing at home and abroad.The firm' s stock price hasbeen bid upward irrationally by individual day traders.Some managers see the currentfren-zy as a spectacularexample ofmarketbubble.The marketbubble can' tbe explained by theaverage rate of growth,butithas reacted on the developmentprospect of high-tech firms.Existing net cash flow method cannot properly capture …     

A two-stage fuzzy robust integer programming approach for capacity planning of environmental management systems

In this study, a two-stage fuzzy robust integer programming (TFRIP) method has been developed for planning environmental management systems under uncertainty. This approach integrates techniques of robust programming and two-stage stochastic programming within a mixed integer linear programming framework. It can facilitate dynamic analysis of capacity-expansion planning for waste management facilities within a multi-stage context. In the modeling formulation, uncertainties can be presented in terms of both possibilistic and probabilistic distributions, such that robustness of the optimization process could be enhanced. In its solution process, the fuzzy decision space is delimited into a more robust one by specifying the uncertainties through dimensional enlargement of the original fuzzy constraints. The TFRIP method is applied to a case study of long-term waste-management planning under uncertainty. The generated solutions for continuous and binary variables can provide desired waste-flow-allocation and capacity-expansion plans with a minimized system cost and a maximized system feasibility.     

Stochastic modelling of reservoir operations

The nature of hydrologic parameters in reservoir management models is uncertain. In mathematical programming models the uncertainties are dealt with either indirectly (sensitivity analysis of a deterministic model) or directly by applying a chance-constrained type of formulation or some of the stochastic programming techniques (LP and DP based models). Various approaches are reviewed in the paper. Moran's theory of storage is an alternative stochastic modelling approach to mathematical programming techniques. The basis of the approach and its application is presented. Reliability programming is a stochastic technique based on the chance-constrained approach, where the reliabilities of the chance constraints are considered as extra decision variables in the model. The problem of random event treatment in the reservoir management model formulation using reliability programming is addressed in this paper.     

An approximate solution approach for a scenario-based capital budgeting model

Real options techniques such as contingent claims analysis and dynamic programming can be used for project evaluation when the project develops stochastically over time and the decision to invest into this project can be postponed. Following that perspective, Meier et al. (Oper Res 49(2):196–2 06, 2001) presented a scenario based model that captures risk uncertainty and managerial flexibility, maximizing the time-varying of a portfolio of investment options. However, the corresponding linear integer program turns out to be quite intractable even for a small number of projects and time periods. In this paper, we propose a heuristic approach based on an alternative scenario based model involving a much less number of variables. The new approach allows the determination of reasonable quality approximate solutions with huge reductions on the computational times required for solving large size instances.     

Hysteresis effects under CIR interest rates

Most decision making research in real options focuses on revenue uncertainty assuming discount rates remain constant. However, for many decisions revenue or cost streams are relatively static and investment is driven by interest rate uncertainty, for example the decision to invest in durable machinery and equipment. Using interest rate models from Cox et al. (1985b), we generalize the work of Ingersoll and Ross (1992) in two ways. Firstly, we include real options on perpetuities (in addition to zero coupon cash flows). Secondly, we incorporate abandonment or disinvestment as well as investment options, and thus model interest rate hysteresis (parallel to revenue uncertainty in Dixit (1989a)). Under stochastic interest rates, economic hysteresis is found to be significant, even for small sunk costs.     

A mixed integer programming model for multistage mean–variance post-tax optimization

In this paper, we introduce a mixed integer stochastic programming approach to mean–variance post-tax portfolio management. This approach takes into account of risk in a multistage setting and allows general withdrawals from original capital. The uncertainty on asset returns is specified as a scenario tree. The risk across scenarios is addressed using the probabilistic approach of classical stochastic programming. The tax rules are used with stochastic linear and mixed integer quadratic programming models to compute an overall tax and return-risk efficient multistage portfolio. The incorporation of the risk term in the model provides robustness and leads to diversification over wrappers and assets within each wrapper. General withdrawals and risk aversion have an impact on the distribution of assets among wrappers. Computational results are presented using a study with different scenario trees in order to show the performance of these models.     

Valuation of project portfolios: An endogenously discounted method

Real options analysis (ROA) has been developed to value assets in which managerial flexibilities create significant value. The methodology is ideal for the valuation of projects in which frequent adjustments (e.g. investment deferral, project scope changes, etc) are necessary in response to the realization of market and technological uncertainties. However, ROA has no practical application when valuing portfolios of multiple concurrent projects sharing resources, as the size of the problem grows exponentially with the number of projects and the length of the time horizon. In this paper an extension of ROA suitable for the valuation of project portfolios with substantial technological uncertainty (e.g. R&D portfolios) is proposed. The method exploits the distributed decision making strategy encountered in most organizations to decompose the portfolio valuation problem into a decision-making sub-problem and a set of single project valuation sub-problems that can be sequentially solved. Discrete event simulation is used for the first sub-problem, while a tailored ROA based strategy is used for the set of valuation sub-problems. A case study from the pharmaceutical industry is used to compare the decision tree analysis (DTA) method and the proposed method.     

Stochastic programming approach to optimization under uncertainty

In this paper we discuss computational complexity and risk averse approaches to two and multistage stochastic programming problems. We argue that two stage (say linear) stochastic programming problems can be solved with a reasonable accuracy by Monte Carlo sampling techniques while there are indications that complexity of multistage programs grows fast with increase of the number of stages. We discuss an extension of coherent risk measures to a multistage setting and, in particular, dynamic programming equations for such problems.      

Multi-stage IT project evaluation: The flexibility value obtained by implementing and resolving Berk, Green and Naik (2004) model

In this paper, we evaluate a multi-stage information technology investment project, by implementing and resolving Berk, Green and Naik’s (2004) model, which takes into account specific features of IT projects and considers the real option to suspend investment at each stage. We present a particular case of the model where the project value is the solution of an optimal control problem with a single state variable. In this case, the model is more intuitive and tractable. The case study confirms the practical potential of the model and highlights the importance of the real-option approach compared to classical discounted cash flow techniques in the valuation of IT projects.     

需求随机下房地产开发商最优进入-退出与能力扩张决策模型

在租赁市场上,房地产开发商常常需要同时决定进入-退出时机及开发能力扩张的的时机.然而这一研究在已往的房地产投资有关文献中有所忽视.鉴于此,在需求随机的条件下,通过一两阶段决策模型同时研究了房地产开发商在租赁市场的进入-退出及能力扩张问题.指出了进入、退出决策的隐式解并给出了扩张决策的阀值及扩张投资额度.研究同时得出结论:不确定性与成本的提高会增大了开发商进入-退出的决策刚性,并同时抑制了开发商的扩张投资.文章同时在行文中分析了结论的经济含义与政策含义.     

Valuing interdependent multi-stage IT investments: A real options approach

In this paper, we use the market asset disclaimer assumption and develop a binomial lattice based real options model to include cash flow interdependencies between multi-stage information technology (IT) investments. Using a simple two-stage IT investment problem with interdependent cash flows, we apply the binomial lattice based real options model to obtain combined valuation of the two-stage IT investment. In addition to investment valuation, our experience with the two-stage IT investment valuation suggests that the binomial lattice based real options model provides a powerful decision aid tool for appropriate timing, delaying and abandoning of the second-stage IT investment.     

Approaches to multistage one-shot decision making

In this research, multistage one-shot decision making under uncertainty is studied. In such a decision problem, a decision maker has one and only one chance to make a decision at each stage with possibilistic information. Based on the one-shot decision theory, approaches to multistage one-shot decision making are proposed. In the proposed approach, a decision maker chooses one state amongst all the states according to his/her attitude about satisfaction and possibility at each stage. The payoff at each stage is associated with the focus points at the succeeding stages. Based on the selected states (focus points), the sequence of optimal decisions is determined by dynamic programming. The proposed method is a fundamental alternative for multistage decision making under uncertainty because it is scenario-based instead of lottery-based as in the other existing methods. The one-shot optimal stopping problem is analyzed where a decision maker has only one chance to determine stopping or continuing at each stage. The theoretical results have been obtained.     

An optimistic decision-making in fuzzy environment

Bellman and Zadeh have originated three systems of multistage decision processes in a fuzzy environment: deterministic, stochastic and fuzzy systems. In this article, we consider an optimization problem with an optimistic criterion on a fuzzy system. By making use of minimization–maximization expectation in a fuzzy environment, we derive a recursive equation for the fuzzy decision process through invariant imbedding approach. By illustrating a three-state, two-decision and two-stage model, we give an optimal solution through dynamic programming. The optimal solution is also verified by the method of multistage fuzzy decision tree-table.