Research On M-V Portfolio Optimization Problem With State-dependent Risk Aversion

In the field of finance control, M-V portfolio is always the research focus. However, the major research directions are the choices of time domain, consumption models, portfolio approach, and so on. The research on risk aversion is very few. In consideration of the importance of risk aversion in M-V portfolio, this paper focuses on the following problems.Firstly, since the M-V portfolio with constant risk aversion is time inconsistent, we use extended HJB equation to solve models in discrete time and continuous time respectively. And, we get the expressions of the optimal investment decision and expected wealth.Secondly, considering the real investment market, this paper discusses an improved model in which the risk aversion g is dependent on the current wealth x. Similarly, we use extended HJB equation to solve this model and get the expressions of the optimal investment decision and expected wealth.Finally, we model the M-V portfolio when(x)xg/g =, and get the analytical solution of the optimal investment decision and expected wealth. What’s more, we use this model to simulate an actual portfolio. In the simulation, we choose some important indicators to get some comparison diagrams between the improved model and the original one. The analysis results imply that the improved model reflects the random fluctuations of the real investment market better. For investors, the improved model is applicable.