Optimal consumption—portfolio problem with CVaR constraints

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• 作者：Qingye Zhang ; ^{zhangqingye123@163.com" class="auth_mail" title="E-mail the corresponding author} ; Yan Gao
• 关键词：Dynamic portfolio selection ; Conditional value-at-risk (CVaR) ; Hamilton&ndash ; Jacobi&ndash ; Bellman (HJB) equation ; Logarithmic utility function
• 刊名：Chaos, Solitons & Fractals
• 出版年：2016
• 出版时间：October 2016
• 年：2016
• 卷：91
• 期：Complete
• 页码：516-521
• 全文大小：518 K

文摘

The optimal portfolio selection is a fundamental issue in finance, and its two most important ingredients are risk and return. Merton's pioneering work in dynamic portfolio selection emphasized only the expected utility of the consumption and the terminal wealth. To make the optimal portfolio strategy be achievable, risk control over bankruptcy during the investment horizon is an indispensable ingredient. So, in this paper, we consider the consumption-portfolio problem coupled with a dynamic risk control. More specifically, different from the existing literature, we impose a dynamic relative CVaR constraint on it. By the stochastic dynamic programming techniques, we derive the corresponding Hamilton–Jacobi–Bellman (HJB) equation. Moreover, by the Lagrange multiplier method, the closed form solution is provided when the utility function is a logarithmic one. At last, an illustrative empirical study is given. The results show the distinct difference of the portfolio strategies with and without the CVaR constraints: the proportion invested in the risky assets is reduced over time with CVaR constraint instead of being constant without CVaR constraints. This can provide a good decision-making reference for the investors.