Mean-variance portfolio with wealth and volatility dependent risk aversion

Risk aversion rate plays a significant role in mean-variance portfolio selection. Most existing literature assumes it to be constant or wealth dependent, which is unrealistic. In this study, I contend that it is both wealth and volatility dependent because it varies across economic status: either steady or fluctuated. In addition, I decompose the risk aversion rate into a wealth prudence rate and a volatility prudence rate and investigate their mutual effect on portfolio selection under a continuous-time mean-variance framework. Using Game theoretic approach and asymptotic expansion, I derive the optimal trading rule analytically.