Two Optimal Investment Problems Based On DC Pension Plan

With the aggravation of the aging of the population,investment in pension funds has become a popular choice,including DB and DC pension plans.In recent years,DC pension plans have attracted more and more attention.This thesis studies two optimal investment problems based on DC pension plans.First question to consider premium return the terms and conditions of the optimal investment problem,assuming pension manager members gave money to the pension plan,pension plan manager to put money into financial markets to obtain high yield,financial markets by determine the interest rate risk free cash assets,rolling bonds and stocks,another hypothesis DC pension members need to pay premium in continuous time,bonds and shares to ban short selling.In this thesis,aiming at minimum variance.The dynamic programming principle is used to solve the optimization problem.The second question considers the optimal investment and life insurance purchase of a family under a DC pension plan.This thesis considers two mortality models: the first,a variable mortality model based on the impact of the death of a partner;The second considers a stochastic mortality model.In this thesis,the analytical solution of the optimization problem is given by using the dynamic programming principle.