A new Chance-Variance optimization criterion for portfolio selection in uncertain decision systems
A new Chance-Variance optimization criterion for portfolio selection in uncertain decision systems
复制标题
不确定决策系统中投资组合选择的新机会-方差优化准则
DOI：
10.1016/j.eswa.2011.12.053
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发表时间：
2012-06
影响因子：
8.5
通讯作者：
郝方方
中科院分区：
文献类型：
--
作者：
刘彦奎;武晓莉;郝方方
马科维茨的均值-方差（M-V）模型作为投资组合优化的实用工具得到了广泛的认可，他的开创性工作在文献中得到了广泛的推广。本文的目的是将M-V方法推广到混合决策系统中。本文提出了一种新的机会方差（C-V）准则来描述模糊随机变量的收益。为此，我们建立了两种类型的C-V模型的混合不确定决策系统的投资组合选择问题。第一类C-V模型是在机会约束下最小化总期望收益率的方差;第二类C-V模型是在方差约束下最大化达到预定收益水平的机会。因此，这两类C-V模型反映了投资者对风险的不同态度。考虑了方差和机会分布的计算问题。对于一般的模糊随机收益率，我们提出了一种计算方差和机会分布的近似方法，从而将C-V模型转化为它们的近似模型。当收益率为梯形模糊随机变量时，我们利用方差和机会分布公式将C-V模型转化为等价的随机规划问题。由于等价的随机规划问题在其目标函数和约束函数中包含了大量的概率分布函数，常规的求解方法无法直接求解。在本文中，我们设计了一个启发式算法来解决这些问题。该算法结合了蒙特卡罗（MC）方法和粒子群优化（PSO）算法，其中MC方法用于计算概率分布函数，PSO算法用于求解随机规划问题。最后，我们提出了一个投资组合选择问题，以证明所开发的建模思想和所设计的算法的有效性。我们还通过数值实验比较了我们的投资组合选择问题的建议C-V方法与M-V方法。
The Markowitz’s mean–variance (M–V) model has received widespread acceptance as a practical tool for portfolio optimization, and his seminal work has been widely extended in the literature. The aim of this article is to extend the M–V method in hybrid decision systems. We suggest a new Chance–Variance (C–V) criterion to model the returns characterized by fuzzy random variables. For this purpose, we develop two types of C–V models for portfolio selection problems in hybrid uncertain decision systems. Type I C–V model is to minimize the variance of total expected return rate subject to chance constraint; while type II C–V model is to maximize the chance of achieving a prescribed return level subject to variance constraint. Hence the two types of C–V models reflect investors’ different attitudes toward risk. The issues about the computation of variance and chance distribution are considered. For general fuzzy random returns, we suggest an approximation method of computing variance and chance distribution so that C–V models can be turned into their approximating models. When the returns are characterized by trapezoidal fuzzy random variables, we employ the variance and chance distribution formulas to turn C–V models into their equivalent stochastic programming problems. Since the equivalent stochastic programming problems include a number of probability distribution functions in their objective and constraint functions, conventional solution methods cannot be used to solve them directly. In this paper, we design a heuristic algorithm to solve them. The developed algorithm combines Monte Carlo (MC) method and particle swarm optimization (PSO) algorithm, in which MC method is used to compute probability distribution functions, and PSO algorithm is used to solve stochastic programming problems. Finally, we present one portfolio selection problem to demonstrate the developed modeling ideas and the effectiveness of the designed algorithm. We also compare the proposed C–V method with M–V one for our portfolio selection problem via numerical experiments.
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模糊随机决策系统中的最小风险问题
影响因子：
4.6
作者：
刘彦奎;刘宝碇
通讯作者：
刘宝碇
影响因子：
--
作者：
ZADEH, LA
通讯作者：
ZADEH, LA
影响因子：
5.4
作者：
KONNO, H;YAMAZAKI, H
通讯作者：
YAMAZAKI, H
DOI：
10.1002/9780470172254
发表时间：
1997
期刊：
--
影响因子：
--
作者：
M. Gen;Runwei Cheng
通讯作者：
M. Gen;Runwei Cheng
影响因子：
3.7
作者：
O. Stramer
通讯作者：
O. Stramer