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October  2016, 12(4): 1521-1533. doi: 10.3934/jimo.2016.12.1521

## Optimal asset portfolio with stochastic volatility under the mean-variance utility with state-dependent risk aversion

 1 Department of Mathematics and Statistics, Curtin University, Kent Street, Bentley, Perth, Western Australia 6102, Australia, Australia, Australia, Australia

Received  December 2014 Revised  August 2015 Published  January 2016

This paper studies the portfolio optimization of mean-variance utility with state-dependent risk aversion, where the stock asset is driven by a stochastic process. The sub-game perfect Nash equilibrium strategies and the extended Hamilton-Jacobi-Bellman equations have been used to derive the system of non-linear partial differential equations. From the economic point of view, we demonstrate the numerical evaluation of the suggested solution for a special case where the risk aversion rate is proportional to the wealth value. Our results show that the asset driven by the stochastic volatility process is more general and reasonable than the process with a constant volatility.
Citation: Shuang Li, Chuong Luong, Francisca Angkola, Yonghong Wu. Optimal asset portfolio with stochastic volatility under the mean-variance utility with state-dependent risk aversion. Journal of Industrial & Management Optimization, 2016, 12 (4) : 1521-1533. doi: 10.3934/jimo.2016.12.1521
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