MEAN-VARIANCE PORTFOLIO OPTIMIZATION WITH STATE-DEPENDENT RISK AVERSION
MEAN-VARIANCE PORTFOLIO OPTIMIZATION WITH STATE-DEPENDENT RISK AVERSION
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DOI：
10.1111/j.1467-9965.2011.00515.x
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发表时间：
2014-01-01
影响因子：
1.6
通讯作者：
Zhou, Xun Yu
中科院分区：
文献类型：
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作者：
Bjoerk, Tomas;Murgoci, Agatha;Zhou, Xun Yu
本文的目的是研究连续时间下的均值-方差组合优化问题。由于这个问题是时间不一致的，我们通过将问题置于博弈论框架中并寻找子博弈的完美纳什均衡策略来解决它。这个特殊的问题已经在Basak和Chabakauri中进行了研究，其中作者假设了一个恒定的风险规避参数。这一假设导致均衡控制，其中投资于风险资产的美元金额独立于当前财富，我们认为从经济学的角度来看，这一结果是不现实的。为了得到一个更现实的模型，我们转而研究风险厌恶动态依赖于当前财富的情况。这是一个比具有恒定风险厌恶的问题要复杂得多的问题，但是，使用比约克和穆尔戈奇发展的时间不一致控制的一般理论，我们对一般情况提供了相当详细的分析。特别是，当风险厌恶与财富成反比时，我们提供了一个分析解，其中投资于风险资产的均衡美元金额与当前财富成正比。因此，该模型的均衡比具有恒定风险厌恶的模型的均衡更为合理。
The objective of this paper is to study the mean-variance portfolio optimization in continuous time. Since this problem is time inconsistent we attack it by placing the problem within a game theoretic framework and look for subgame perfect Nash equilibrium strategies. This particular problem has already been studied in Basak and Chabakauri where the authors assumed a constant risk aversion parameter. This assumption leads to an equilibrium control where the dollar amount invested in the risky asset is independent of current wealth, and we argue that this result is unrealistic from an economic point of view. In order to have a more realistic model we instead study the case when the risk aversion depends dynamically on current wealth. This is a substantially more complicated problem than the one with constant risk aversion but, using the general theory of time-inconsistent control developed in Bjork and Murgoci, we provide a fairly detailed analysis on the general case. In particular, when the risk aversion is inversely proportional to wealth, we provide an analytical solution where the equilibrium dollar amount invested in the risky asset is proportional to current wealth. The equilibrium for this model thus appears more reasonable than the one for the model with constant risk aversion.