Optimal investment and benefit payment strategy under loss aversion for target benefit pension plans

Abstract

In this paper, we consider the optimal investment and benefit payment strategy for a target benefit plan (TBP), where the plan members are loss averse with an S-shaped utility over benefit relative to a time-varying target benefit level. The pension payments are dependent on the financial situation of the plan, with risk sharing between different generations. The pension fund is invested in both a risk-free asset and multiple risky assets. Using the martingale method, we derive the optimal investment strategy and optimal benefit payment policy, explicitly, which minimizes the interim utility of the benefit risk in terms of deviating from the benefit target. Finally, some numerical examples and sensitivity analyses are provided to show the effects of market parameters on the optimal strategies. We also compare the optimal benefit payment policy for loss-averse participants with that of constant relative risk averse (CRRA) participants by numerical results. We find that the TBP model for loss-averse participants is effective in providing a stable and sustainable pension account for participants.