The Optimal Portfolio Of Stochastic Factors

Under the premise of perfecting the financial market,this paper improves the existing financial model and tries to use the best mathematical model to describe thereality of the financial market by introducing different stochastic factors.The main contents of the study are as follows:1.The stochastic labor income is introduced into the Vasicek stochastic interest rate model and the explicit solution of the optimal consumption investment strategy is obtained according to the related knowledge such as stochastic control theory and variable substitution.2.The zero-coupon bond is introduced Into the Heston stochastic volatility model.The mathematical model is established by applying the dynamic programming principle and the stochastic control theory.The corresponding HJB equation and the corresponding mathematical model are established by using dynamic programming principle and the consumption strategy in the power utility case.3.According to the general stochastic LQ technique,the optimal investment strategy with stochastic labor income and the corresponding efficient frontier under the mean variance model are obtained.4.According to the idea of stochastic differential game,the equation of the optimal investment strategy of two competitors with the stochastic exchange rate under different utility functions is obtained.