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

Shuang  Li; Chuong  Luong; Francisca  Angkola; Yonghong  Wu

doi:10.3934/jimo.2016.12.1521

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2016, Volume 12, Issue 4: 1521-1533. Doi: 10.3934/jimo.2016.12.1521

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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

Received: November 30, 2014

Revised: July 31, 2015

Published: September 2016

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Abstract

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.

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Mathematics Subject Classification: Primary: 91B16, 91B70, 91G10; Secondary: 91G80.

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