基于不确定性期望效用模型的投资优化  

Portfolio Optimization Based on Generalized Expected Utility Model with Uncertainty

作　　者：马孝先[1] 曲吉林[2] 赵庆祯[3] 

机构地区：[1]山东财经大学金融学院,山东济南250014 [2]山东财经大学会计学院,山东济南250014 [3]山东师范大学公共管理学院,山东济南250014

出　　处：《数学的实践与认识》2014年第18期1-8,共8页Mathematics in Practice and Theory

基　　金：国家自然科学基金(70840018);山东省自然基金课题(ZR2012GM010)

摘　　要：针对资产的收益的分布不确切知道,并且所获得的矩信息也不是准确值的问题,提出了最大化最坏情形期望效用的鲁棒性方法.引入了凹凸类效用函数来度量模型不确定情形下投资者的效用,用一个不确定性结构来刻画资产收益的所有可能的分布和收益的矩信息,通过把具有不确定性结构的鲁棒性模型转化成参数二次规划问题,得到了最优投资策略、有效前沿和均衡价格的解析表示.方法为采用保守策略并且厌恶不确定性的投资者提供了一种有效的投资决策方案.Robust approach maximizing worst-case utility was provided when both the distributions underlying the uncertain vector of returns are exactly unknown and the estimates of the structure of returns are unreliable. They introduced concave convex utility function measuring the utility of investors under model uncertainty and uncertainty structure describing the moments of returns and all possible distributions. Explicit formula solutions of efficient fi＇ontier and equilibrium price system were obtained by reformulating a robust portfolio optimization model with uncertainty structure as a parametric quadratic programming. This approach is an alternative of solving the optimal portfolios for an uncertainty-averse investor who takes a conservative viewpoint and identify asset mixes that have the best worst-case expected utility.

关 键 词：投资优化 有效前沿 数学规划 均衡价格 

分 类 号：F224[经济管理—国民经济] F830.59