Optimal Investment Strategy For The DC Plan With The Return Of Premiums

In China,the phenomenon of aging is becoming more and more prominent,which makes the government pays more attention to the investment of pension.Referring to the development of the pension operation in the world,investment diversification is a big trend.According to the ”pension fund investment management approach” introduced in 2015,the government allows individual pension accounts to invest in equity assets.Under such a background,it is very meaningful to study asset management of the DC plan.This paper studies the time-consistent investment strategy in the DC plan during the accumulation phase.Most of DC plan have return of premium clauses,which means the members withdraw their premiums when they die before retirement and the difference between the premium and accumulation is distributed to other members equally.Meanwhile,there are a risk-free asset and a risky asset whose price is modeled by jump-diffusion process.In the time-consistent framework,considering the transaction costs and taxes,an extended Hamilton-Jacobi-Bellman(HJB)equations of the equilibrium value function is established.The closed-form expression for the time-consistent investment strategy and optimal value function are derived by stochastic control technique.Moreover,the effects of jump-diffusion process on the equilibrium strategy and equilibrium value function are illustrated by mathematical and numerical analysis.The differences of optimal strategies between plan with and without the return of premium are explored via Monte Carlo methods.Finally,based on the real market,we put forward some operating recommendation for fund managers,and some suggestion for the practicability of our model.