多目标优化问题的完全标量化

本文首先利用松弛变量和广义Tchebycheff范数的推广形式提出一类新的标量化优化问题.进一步,通过调整几种参数范围获得一般多目标优化问题弱有效解、有效解和真有效解的一些完全标量化刻画.此外,本文提出例子对主要结果进行说明,利用相应的标量化方法判定给定的多目标优化问题的可行解是否是弱有效解、有效解和真有效解.     

期望和残差收益估计不可靠的鲁棒模型

投资优化问题的最优策略会随着输入参数的扰动而出现敏感的变化,针对投资优化问题中出现的随机变量的参数估计不可靠的情况,本文引入不确定集合描述随机收益的有关矩信息,提出了投资优化问题的一个鲁棒性模型,并采用数学规划的理论和方法,给出了该模型的最优策略和有效前沿的解析表示。本方法能够为采用保守策略的、对不确定性厌恶的投资者提供一种最优的投资策略。     

基于条件VaR(CVaR)的投资组合优化模型及比较研究

在总结投资组合优化模型的基础上 ,详细分析了 Va R和 CVa R的概念及重要性质 ,分析了将 Va R和 CVa R应用于决策问题的处理技巧 .针对传统均值—方差模型 ,提出不考虑各种限定条件的基于条件Va R( CVa R)的投资组合优化模型以及考虑限定条件的一般模型 .针对模型的适用性 ,详细比较了 CVa R模型和均值—方差模型的应用复杂性 ,并利用实际数据进行了对比 .     

均值-方差准则下的多期最优保险投资(英文)

近年来,最优保险投资问题吸引了越来越多的注意。一般这个问题是在连续时间框架下来研究的。本文针对这一问题建立离散时间的最优控制模型。应用动态规划原理求解模型对应的近似问题,得到了最优投资策略和投资有效边界的解析表达形式。本文得到的最优投资策略和投资有效边界均依赖于承保参数。通过数值例子分析了承保参数对最优投资策略和有效边界的影响。     

Growth-security profiles in capital accumulation under risk

This paper considers the tradeoff between growth and security in the problem of capital accumulation under risk. It is shown how growth can be continuously traded for security with simple deterministic strategies generated from the optimal growth and optimal security problems. A lower bound is derived for the error resulting from the use of such strategies.     

OPTIMALITY CONDITIONS AND APPROXIMATE OPTIMALITY CONDITIONS IN LOCALLY LIPSCHITZ VECTOR OPTIMIZATION

Abstract

In this paper, we study constrained locally Lipschitz vector optimization problems in which the objective and constraint spaces are Hilbert spaces, the decision space is a Banach space, the dominating cone and the constraint cone may be with empty interior. Necessary optimality conditions for this type of optimization problems are derived. A sufficient condition for the existence of approximate efficient solutions to a general vector optimization problem is presented. Necessary conditions for approximate efficient solutions to a constrained locally Lipschitz optimization problem is obtained.     

证券集的组合前沿分类与有效子集

本文通过引入证券价格 ,讨论一般证券集组合前沿的分类 ,并据此直接证明判定某个证券子集是全集的有效子集的一个充要条件     

An all-linear programming relaxation algorithm for optimizing over the efficient set

The problem (P) of optimizing a linear function over the efficient set of a multiple objective linear program has many important applications in multiple criteria decision making. Since the efficient set is in general a nonconvex set, problem (P) can be classified as a global optimization problem. Perhaps due to its inherent difficulty, it appears that no precisely-delineated implementable algorithm exists for solving problem (P) globally. In this paper a relaxation algorithm is presented for finding a globally optimal solution for problem (P). The algorithm finds an exact optimal solution to the problem after a finite number of iterations. A detailed discussion is included of how to implement the algorithm using only linear programming methods. Convergence of the algorithm is proven, and a sample problem is solved.Research supported by a grant from the College of Business Administration, University of Florida, Gainesville, Florida, U.S.A.     

不同均值-风险准则下的资产组合有效前沿比较研究

本文根据V aR和CV aR风险度量方法,对马克维茨的均值-方差资产组合选择模型进行拓展,研究在均值-风险准则下更具有一般性的资产组合选择问题.并在正态分布假设条件下,证明当不存在无风险资产时和存在无风险资产时,基于方差、V aR和CV aR风险度量准则的资产组合有有沿之间的关系,指出根据均值-V aR准则和均值-CV aR准则求解有效资产组合时,置信水平必须满足的条件     

Single-Period Markowitz Portfolio Selection,Performance Gauging,and Duality: A Variation on the Luenberger Shortage Function

The Markowitz portfolio theory (Ref. 1) has stimulated research into the efficiency of portfolio management. This paper studies existing nonparametric efficiency measurement approaches for single-period portfolio selection from a theoretical perspective and generalizes currently used efficiency measures into the full mean-variance space. We introduce the efficiency improvement possibility function (a variation on the shortage function), study its axiomatic properties in the context of the Markowitz efficient frontier, and establish a link to the indirect mean-variance utility function. This framework allows distinguishing between portfolio efficiency and allocative efficiency; furthermore, it permits retrieving information about the revealed risk aversion of investors. The efficiency improvement possibility function provides a more general framework for gauging the efficiency of portfolio management using nonparametric frontier envelopment methods based on quadratic optimization.     

Parametric vector optimization

In this paper we consider a sequence of vector optimization problems. We aim to generalize a vector condition that relates the parametric function and the limit function. In particular, we recover our condition given in the scalar case. Our stability approach is such that the limit of the sequence of solutions that correspond to vector optimization problems to be a solution of a limit vector optimization problem. Therefore, one can view our statement as an existence result. This general framework has been used in several previous works. In our main theorem, we use the notion of strong lower cone-semi-continuity. An example is given to illustrate why only cone-lower semi-continuity for the limit function is not sufficient for our result.     

Calmness and Exact Penalization in Vector Optimization with Cone Constraints

In this paper, a (local) calmness condition of order α is introduced for a general vector optimization problem with cone constraints in infinite dimensional spaces. It is shown that the (local) calmness is equivalent to the (local) exact penalization of a vector-valued penalty function for the constrained vector optimization problem. Several necessary and sufficient conditions for the local calmness of order α are established. Finally, it is shown that the local calmness of order 1 implies the existence of normal Lagrange multipliers. Presented at the 6th International Conference on Optimization: Techniques and Applications, Ballarat, Australia, December 9–11, 2004 This work is supported by the Postdoctoral Fellowship of Hong Kong Polytechnic University.     

Sensitivity Analysis of Multiobjective Optimization Problems with Parameterized Quasi-Variational Inequalities

This paper mainly establishes the sensitivity analysis of a multiobjective optimization problem with parameterized quasi-variational inequalities (QVIs). Using the (regular) coderivative of the associated epigraphical multifunction, the (regular) subdifferentials of the efficient frontier maps are estimated, which involve the (regular) coderivatives of the solution mapping to the parameterized QVIs. Under the linear independent constraint qualification, the defined auxiliary set-valued mappings in the parameterized QVIs are clam. The detailed formulae of subdifferentials of the efficient frontier maps are obtained and examples are simultaneously provided for analyzing and illustrating the obtained results.     

Markov-modulated mean-variance problem for an insurer

In this paper, we consider an insurance company which has the option of investing in a risky asset and a risk-free asset, whose price parameters are driven by a finite state Markov chain. The risk process of the insurance company is modeled as a diffusion process whose diffusion and drift parameters switch over time according to the same Markov chain. We study the Markov-modulated mean-variance problem for the insurer and derive explicitly the closed form of the efficient strategy and efficient frontier. In the case of no regime switching, we can see that the efficient frontier in our paper coincides with that of [10] when there is no pure jump.     

任意收益率分布和奇导协方差矩阵下的均值——风险模型研究

本文在一般均值-风险模型的框架下,在无套利假设下研究了奇异协方差矩阵和任意收益率分布情形下的投资组合问题,得到了模型有效边界的本质特征,并给出了极大线性无关组的确定方法及表示系数的求解方法,最后根据这些结论提出了有效的、操作性强的投资策略。     

Further study on the Levitin-Polyak well-posedness of constrained convex vector optimization problems

In this paper, we first establish characterizations of the nonemptiness and compactness of the set of weakly efficient solutions of a convex vector optimization problem with a general ordering cone (with or without a cone constraint) defined in a finite dimensional space. Using one of the characterizations, we further establish for a convex vector optimization problem with a general ordering cone and a cone constraint defined in a finite dimensional space the equivalence between the nonemptiness and compactness of its weakly efficient solution set and the generalized type I Levitin-Polyak well-posednesses. Finally, for a cone-constrained convex vector optimization problem defined in a Banach space, we derive sufficient conditions for guaranteeing the generalized type I Levitin-Polyak well-posedness of the problem.     

借贷利率限制下资产-负债管理问题的均值-方差模型

将负债过程和借款利率限制引入投资组合优化问题中,并建立该问题的均值-方差模型.通过引入拉格朗日函数并应用拉格朗日对偶定理得到一个等价的新的优化模型,然后应用动态规划原理得到了最优投资策略和有效前沿的解析表达式.算例解释了所得结论.     

两类锥广义伪不变凸性的刻画

研究了一类非光滑带约束的向量优化问题. 首先引入锥意义下的 FJ-伪不变凸I(II)型的概念; 然后将经典的Gordan择一定理推广到了带锥的情形,并在此基础上利用FJ向量驻点与(弱)有效解间的关系, 研究了锥FJ-伪不变凸I(II)型的等价刻画.     

多目标最优化G-恰当有效解集的存在性和连通性

本文证明了非空紧凸集上拟凸多目标最优化问题的G-恰当有效解的存在性．在此基础上，得到了向量目标函数既是似凸又是拟凸的多目标最优化问题的G-恰当有效解集是连通的结论．同时，还给出一个关于Pareto有效解集连通性的新结果．     

A graphical characterization of the efficient set for?convex multiobjective problems

In this paper, a graphical characterization, in the decision space, of the properly efficient solutions of a convex multiobjective problem is derived. This characterization takes into account the relative position of the gradients of the objective functions and the active constraints at the given feasible solution. The unconstrained case with two objective functions and with any number of functions and the general constrained case are studied separately. In some cases, these results can provide a visualization of the efficient set, for problems with two or three variables. Besides, a proper efficiency test for general convex multiobjective problems is derived, which consists of solving a single linear optimization problem.