Optimal investment strategies and intergenerational risk sharing for target benefit pension plans under habit formation

This paper investigates a stochastic model of a continuous-time target benefit pension system with habit formation, where members' contributions are predetermined and pension payments depend on the financial condition of the system. Moreover, risk sharing among different generations is considered and we incorporate the habitual benefit payment process into the plan manager's objective. Concretely, the plan manager aims to minimize the deviation between actual payments and habitual payments, which can minimize the combined benefit-risk (i.e. deviation from the habitual target) and intergenerational transfers effectively. Furthermore, the pension fund is allowed to invest in a risk-free asset and a risky asset. By employing the martingale method, we derive the optimal investment strategy and the benefit adjustment strategy explicitly. Finally, numerical analysis is provided to illustrate the effects of model parameters on the optimal strategies.