Optimal Portfolio Problem Under The Influence Of Stachastic Factors

Portfolio optimization problem is an important research content in the mathematical finance,which is crucial for investors under the variability of the market uncertainty and investment environment to make them in the risk tolerance range to obtain the maximum benefit.According to the different investment environment,this paper mainly studies five problems and analyzes its financial significance briefly.Firstly,we study portfolio consumption problem with non tradable risk assets under the imperfect market.The incomplete market is translated into the complete market by adding virtual stocks.The optimal consumption and investment strategy of virtual financial market is the optimal investment and consumption strategies of ornginal financial market problems under certain conditions by using martingale method and combining the duality theory.Secondly,we mainly study random consumption following Ho-Lee model and the analytic expression of the optimal investment strategy of the power utility function is obtained by applying dynamic programming prnnciple.And through the comparison of the three cases of non consumption,constant interest rates and fixed consumption of investment strategies,the power utility function of the investor's optimal investment strategy is closely related to the stochastic interest rate and random consumption process.Thirdly,analyzing the optimal investment strategy with minimum performance constraints based on dynamic reference point in a complete market,the random reference point is equivalent to another loss averse level under the fixed reference point by using equivalent transformation.We derive the analytical expression of optimal risky asset weight by applying the martingale method,based on which we obtain the expected optimal terminal wealth of loss aversion investors whose reference point is dynamically adjusted.Furthermore,we study liabilities of M-V portfolio investment based on the Vasicek interest rate model and the HJB equation of the value function is obtained by applying dynamic programming principle and introducing auxiliary problem.Then the closed-form solutions to the optimal investment strategy and effctive frontier are obtained by applying Legendre transform and variable change techniques.Then the results are analyzed on optimal investment strategy.