Insurer’s Optimal Investment Policy Under Diffusion Approximations And Perturbed Stochastic Factors

This thesis studies the insurance company’s choice of optimal investment strategy,when they have uncontrollable random cash flow and the underlying stock is affected by stochastic factors,which maximizes utility of the terminal wealth.We consider a class of stochastic factor processes with single factor or mixed factors.The single factor model includes the singular perturbed factor or the regular perturbed factor,while the mixed factor model is driven by singular and regular factors simultaneously.The company’s wealth is affected by random risk and the stock being invested is driven by stochastic factors.The problem of maximum utility of terminal wealth is converted to a nonlinear Hamilton-Jacobi-Bellman PDE problem via the dynamic programming principle,and the asymptotic analysis method is used to approximate the solution.When the utility function is an exponential utility function,the second-order analytical solution of the value function under single factor model and mixed factor model are solved respectively,and then the second-order analytical solution of the investment strategy can be obtained.Under the exponential utility function,the wealth variable in the value function can be separated from other variables,and hence the nonlinear PDE problem can be transformed into a linear PDE problem,and the asymptotic analysis of the value function of the linear PDE problem is performed.Finally,an accuracy analysis for the second-order analytical solution of the original value function is achieved.This thesis assesses the approximation for the second-order asymptotic solutions of the value function and the optimal strategy in a particular case where there is an explicit solution.