Study On Several Types Of Financial Models Based On Stochastic Control Theory

With the development of domestic economy and the aging of population,the oldage insurance system is playing a more and more important role in the social security system.Reasonable allocation of pension funds in the financial markets is related to the standard of living of the pension after retirement plan participants,so the optimal investment strategy of the pension is a hot issue in the field of finance.However,in the actual financial market,there are more than one kind of risky assets,and the income and variance are stochastic.Therefore,it will be more practical to study the optimal investment strategies for multiple risky assets under the circumstance of stochastic interest rates and stochastic volatility.Based on stochastic optimal control theory,stochastic differential equation,martingale theory and separation variable technique,the optimal investment problem of DC pension is studied,the main research contents and results are as follows:First of all,the optimal investment strategy is studied when the price process of risky assets obeys the constant square elasticity(CEV)model.The pension fund is invested in a risk-free asset and n risky assets.Taking model uncertainty risk into consideration,the optimal control problem is transformed into a problem of maximizing the minimal expected exponential utility of terminal wealth,Based on the stochastic control theory,the Hamilton-Jacobi-Bellman(HJB)equation is obtained,and the optimal investment strategy is obtained under the exponential utility function.Based on the theory of stochastic differential equations,value function verification theorem is given.Under the circumstance of stochastic interest rate and stochastic income,the optimal control model is reestablished,and the corresponding HJB equation is obtained.The optimal investment strategy is obtained under the power utility function.Secondly,the optimal investment strategy is studied when the price process of two risky assets obeys the Heston'SV model.Taking model uncertainty risk into consideration,the optimal investment strategy is obtained under the exponential utility function.After introducing stochastic income,the optimal control model is reestablished,and the corresponding HJB equation is solved under the power utility function,and the optimal investment strategy is obtained.The numerical results show that the risk aversion coefficient,the ambiguity aversion coefficient and the model parameters have a certain influence on the optimal investment strategy.Finally,the optimal investment strategy is studied when the price process of two risky assets obeys the Stein-Stein model.The model uncertainty risk is still considered.Under the exponential utility function and the power utility function,the optimal invest-ment strategy is obtained under the condition of constant contribution rate and stochastic income.The numerical results are analyzed and a conclusion similar to that of Heston'SV model is obtained.