Second Order Fast And Slow Stochastic Factors Asymptotics Of Portfolio Optimization

The portfolio model affected by stochastic factors has been investigated by many scholars and has been achieved fruitful research results.Based on stochastic control theory,this thesis studies a kind of portfolio model with stochastic fast and slow factors.We extend the approximate solution of the value function and the optimal strategy for the model in the literature to the second order.This problem is a singular perturbation problem.We construct a formal asymptotic solution according to the partial differential equation of value function and some property of poisson equation.We then prove the asymptotic parabolic solution of value function is polynomial decay by accuracy analysis.In the process of accuracy analysis,we also prove that the solutions of a class of nonlinear partial differential equations can be expressed by the solutions of a class of linear partial differential equations.Finally,we use the examples to show that the second-order asymptotic solutions of the value function and optimal strategy are accurate via numerical simulation.