多周期多目标条件风险值模型

在商业、工业、电力和房地产等行业中存在许多复杂的多周期风险决策问题,它的数学模型研究对于解决这些问题具有重要的作用.作者建立了一种新的多周期多目标条件风险值(CVaR)数学模型理论和方法.先定义了一种带时间段的多周期多目标损失函数下的α-VaR和α-CVaR值,给出了一类多周期多目标CVaR最优化模型.然后,证明了多目标意义下的对应模型的等价定理,给出了多周期多目标CVaR模型的近似求解等价模型.最后,建立了一种生产企业在供过于求和供不应求两种情形下产生的多周期双目标CVaR模型,针对一个电力生产企业进行的数值实验,表明了模型可以得到在最小供给的用电损失分布下的各周期下的相匹配供电策略,可以帮助供电部门各个时期供电不平衡状况下的风险控制.     

多目标条件风险值问题的等价定理

条件风险值问题是研究信用风险最优化的一种新的模型，本文研究了一类多目标条件风险值问题等价定理，我们引入了多个损失函数在对应的置信水平下关于一个证券组合的α-VaR损失值(最小信用风险值)和α-CVaR损失值(最小信用风险值对应的条件期望损失值或条件风险价值度量)概念，为了求得α-CVaR损失值下的弱：Pareto有效解，我们证明了它等价于求解另一个多目标规划问题的Pateto有效解，这样使得问题的求解变得简单．     

多目标条件风险值的一种近似求解方法

本文研究了一种求解多目标条件风险值问题的近似方法,首先引入了多个损失函数在对应的置信水平下关于一个证券组合的α-VaR损失值,以及α-CVaR损失值概念．α-CVaR损失值表明了在给定的证券组合于置信水平对应的最小信用风险值的条件期望损失值,那么求出这样的最小条件期望损失值的模型构成了一个求解α-CVaR损失值的多目标问题,它的解就是最小条件期望损失值的有效证券组合,即Pareto弱有效解．为了求解它的Pareto弱有效解,我们引进了损失函数对应的优化问题(SCVaR),可以通过求解非线性规划问题(SCVaR)的最优解近似地刻画α—CVaR损失值,这样使得求解α-CVaR损失值变得容易．     

基于多目标CVaR模型的证券组合投资的风险度量和策略

本文首先定义了多损失函数下的-αVaR,-αCVaR损失值以及-αCVaR损失值的等价函数,给出了多目标CVaR模型.然后,基于多目标CVaR模型,建立了一个多目标证券组合投资优化模型,得出在多置信水平下的证券组合投资比例和CVaR值,据此建立一种证券组合投资的降低风险优化模型.其降低风险策略是在收益率不变的情形下降低风险和总投资比例.数值实验表明,这种策略是可以通过明显地减少总投资比例来达到降低风险的目的.     

一种多随从双层条件风险值模型的等价性定理

多随从风险决策问题是供应链风险决策中普遍存在的问题,文章研究了风险厌恶下的多随从双层条件风险值模型,引入了多随从上下层决策的VaR损失值(最小风险值)和CVaR损失值(最小风险值对应的条件期望损失值或条件风险价值度量)概念,提出了一种风险厌恶下的多随从双层条件风险值模型,该模型的目标是求上下层的基于权值的多损失CVaR达最小的最优解,文章证明了它可以通过另一个较容易求解的双层规划模型获得最优解的等价性定理.     

多损失条件风险值的多层规划模型

对于多个损失函数,在给定的置信水平下,首先定义了不超过给定损失值的最小风险值(即Va R值)和基于权值的累积期望损失值(即CVa R损失值)概念,然后建立了一个多损失条件风险值的多层规划模型.该模型的目标是求各层多损失CVa R值达最小的最优策略,并证明了它等价于另一个较容易求解的多层规划模型.最后,给出了三级供应链中多产品的定价与订购的条件风险值模型(三层线性规划模型).     

协方差矩阵退化情形均值-CVaR模型的有效边界

本文利用CVaR方法代替方差或CVaR来度量风险,建立了均值-CVaR模型,首先利用等CVaR线的方法研究了包含无风险资产的均值-CVaR模型的有效边界,然后在无套利假设下研究了当风险资产的协方差矩阵是奇异时的均值-CVaR模型,并得到了正态情形下模型的有效边界及其解析表达式.     

基于均值和CVaR的效用最大化模型研究

本文利用CVaR方法代替方差或VaR来度量风险,建立了关于期望和CVaR的效用最大化模型,研究了n种风险资产的投资决策问题。在效用函数是凹的假设下,首先得到了无差异曲线的特征及均值-CVaR模型有效边界的性质,然后利用这些结论得到了效用最大值存在的条件及其最优解的性质特征,给出了求解的具体步骤和算法,并分析了最大效用点的经济含义.最后,一个基于中国股票市场真实数据的数值算例说明了本文的结论及应用。     

规避风险的多阶段最优库存研究

基于市场需求是随机的,并且在进行市场销售前,就要确定每个阶段的生产数量的背景下,建立了具有规避风险的多阶段库存凸随机规划模型.该模型以最小化损失函数的期望值为目标函数,以规避风险为约束条件,以价值风险(VaR)和条件价值风险(CVaR)为风险度量;采用样本平均近似方法(SAA)求解该模型,并分析样本平均近似方法的收敛性;最后,给出数值结果.     

基于CVaR投资组合优化问题的光滑化方法

对选定的风险资产进行组合投资,以条件风险价值(CVaR)作为度量风险的工具,建立单期投资组合优化问题的CVaR模型。目标函数中含有多重积分与plus函数,产生情景矩阵将多重积分计算转化成求和运算,提出plus函数的一个新的一致光滑逼近函数并给出求解CVaR模型的光滑化方法,最后的实证研究表明了本文算法的优越性。     

Asymptotic Analysis of Sample Average Approximation for Stochastic Optimization Problems with Joint Chance Constraints via Conditional Value at Risk and Difference of Convex Functions

Conditional Value at Risk (CVaR) has been recently used to approximate a chance constraint. In this paper, we study the convergence of stationary points, when sample average approximation (SAA) method is applied to a CVaR approximated joint chance constrained stochastic minimization problem. Specifically, we prove under some moderate conditions that optimal solutions and stationary points, obtained from solving sample average approximated problems, converge with probability one to their true counterparts. Moreover, by exploiting the recent results on large deviation of random functions and sensitivity results for generalized equations, we derive exponential rate of convergence of stationary points. The discussion is also extended to the case, when CVaR approximation is replaced by a difference of two convex functions (DC-approximation). Some preliminary numerical test results are reported.     

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.     

Newsvendor solutions via conditional value-at-risk minimization

In this paper, we consider the minimization of the conditional value-at-risk (CVaR), a most preferable risk measure in financial risk management, in the context of the well-known single-period newsvendor problem, which is originally formulated as the maximization of the expected profit or the minimization of the expected cost. We show that downside risk measures including the CVaR are tractable in the problem due to their convexity, and consequently, under mild assumptions on the probability distribution of products’ demand, we provide analytical solutions or linear programming (LP) formulation of the minimization of the CVaR measures defined with two different loss functions. Numerical examples are also exhibited, clarifying the difference among the models analyzed in this paper, and demonstrating the efficiency of the LP solutions.     

基于动态损失厌恶投资组合优化模型及实证研究

为了研究行为金融学中损失厌恶的心理特征对投资决策的影响,建立预期效用最大化的动态损失厌恶投资组合优化模型。以我国股票市场为依托进行实证研究,将市场分为上升、下降和盘整三种状态,研究动态损失厌恶投资组合模型的表现,与静态损失厌恶投资组合模型、均值-方差投资组合模型和CVaR投资组合模型进行比较。通过改变参照点对动态模型进行稳健性检验。得出动态损失厌恶投资组合模型优于静态模型、均值-方差投资组合模型和CVaR投资组合模型的结论。     

Preference modelling by estimating local utility functions for multiobjective optimization

This paper is intended to design goal programming models for capturing the decision maker's (DM's) preference information and for supporting the search for the best compromise solutions in multiobjective optimization. At first, a linear goal programming model is built to estimate piecewise linear local utility functions based on pairwise comparisons of efficient solutions as well as objectives. The interactive step trade-off method (ISTM) is employed to generate a typical subset of efficient solutions of a multiobjective problem. Another general goal programming model is then constructed to embed the estimated utility functions in the original multiobjective problem for utility optimization using ordinary nonlinear programming algorithms. This technique, consisting of the ISTM method and the newly investigated search process, facilitates the identification and elimination of possible inconsistent information which may exist in the DM's preferences. It also provides various ways to carry out post-optimality analysis to test the robustness of the obtained best solutions. A modified nonlinear multiobjective management problem is taken as example to demonstrate the technique.     

Higher-Order Duality in Nondifferentiable Multiobjective Programming

A new generalized class of higher-order (F, α, ρ, d)–type I functions is introduced, and a general Mond–Weir type higher-order dual is formulated for a nondifferentiable multiobjective programming problem. Based on the concepts introduced, various higher-order duality results are established. At the end, some special cases are also discussed.     

On duality theory in multiobjective programming

In this paper, we study different vector-valued Lagrangian functions and we develop a duality theory based upon these functions for nonlinear multiobjective programming problems. The saddle-point theorem and the duality theorem are derived for these problems under appropriate convexity assumptions. We also give some relationships between multiobjective optimizations and scalarized problems. A duality theory obtained by using the concept of vector-valued conjugate functions is discussed.The author is grateful to the reviewer for many valuable comments and helpful suggestions.     

A new multiobjective simulated annealing algorithm

A new multiobjective simulated annealing algorithm for continuous optimization problems is presented. The algorithm has an adaptive cooling schedule and uses a population of fitness functions to accurately generate the Pareto front. Whenever an improvement with a fitness function is encountered, the trial point is accepted, and the temperature parameters associated with the improving fitness functions are cooled. Beside well known linear fitness functions, special elliptic and ellipsoidal fitness functions, suitable for the generation on non-convex fronts, are presented. The effectiveness of the algorithm is shown through five test problems. The parametric study presented shows that more fitness functions as well as more iteration gives more non-dominated points closer to the actual front. The study also compares the linear and elliptic fitness functions. The success of the algorithm is also demonstrated by comparing the quality metrics obtained to those obtained for a well-known evolutionary multiobjective algorithm.     

An interactive fuzzy satisficing method for multiobjective 0–1 programming problems with fuzzy numbers through genetic algorithms with double strings

In this paper, by considering the experts' vague or fuzzy understanding of the nature of the parameters in the problem-formulation process, multiobjective 0–1 programming problems involving fuzzy numbers are formulated. Using the a-level sets of fuzzy numbers, the corresponding nonfuzzy α-programming problem is introduced. The fuzzy goals of the decision maker (DM) for the objective functions are quantified by eliciting the corresponding linear membership functions. Through the introduction of an extended Pareto optimality concept, if the DM specifies the degree α and the reference membership values, the corresponding extended Pareto optimal solution can be obtained by solving the augmented minimax problems through genetic algorithms with double strings. Then an interactive fuzzy satisficing method for deriving a satisficing solution for the DM efficiently from an extended Pareto optimal solution set is presented. An illustrative numerical example is provided to demonstrate the feasibility and efficiency of the proposed method.