Nash Equilibrium Strategy for a DC Pension Plan with State-Dependent Risk Aversion: A Multiperiod Mean-Variance Framework

Abstract

This paper investigates a defined contribution (DC) pension plan investment problem during the accumulation phase under the multiperiod mean-variance criterion. Different from most studies in the literature, where the investor's risk aversion attitude is state-independent, we choose a state-dependent risk aversion parameter, which is a fractional function of the current wealth level. Moreover, we incorporate the wage income factor into our model, which leads to a more complicated problem than the portfolio selection problems that appeared in relevant papers. Due to the time inconsistency of the resulting problem, we derive the explicit expressions for the equilibrium strategy and the corresponding equilibrium value function by adopting the game theoretic framework and using the extended Bellman equation. Further, two special cases are discussed. Finally, based on real data from the American market, some prominent features of the equilibrium strategy established in our theoretical derivations are provided by comparing them with the results in the existing literature.Hindawi

Robust equilibrium control-measure policy for a DC pension plan with state-dependent risk aversion under mean-variance criterion

“…It is worth noting that the robust equilibrium policy (39)- (41) obtained in this case is essentially the same as that given in Pun [37] (i.e., the case of state-dependent risk aversion).…”

“…Hu et al [18] define the risk aversion as a linear function of the current wealth level in a continuous-time setting. Wu [44] and Wang and Chen [41] adopt the same model for the risk aversion parameter as that in Björk et al [5] and investigate the optimal policy for the portfolio selection and DC pension plans in discrete-time, respectively. Cui et al [12] and Cui et al [13] propose a flexible behavioral risk aversion model which takes a piece-wise linear form of the surplus or shortage with respect to a preset investment target in the continuous-time setting and the multi-period setting, respectively.…”

Stochastic Game Theoretic Formulation for a Multi-Period DC Pension Plan with State-Dependent Risk Aversion

“…Like Wu [12], the similar problem arises again: when the wealth level is less than a certain value, the risk aversion parameter becomes negative. Following the work of Wu [12], Wang and Chen [14] investigate the optimal investment for a DC pension plan in a multi-period setting. Unfortunately, there are still irrational situations in their work.…”

“…As mentioned above, the main goal of this paper is to further improve the work of Wang and Chen [14]. Noting the importance of the positiveness nature of the wealth process in a discrete-time setting, we hope to modify the wealth process to ensure its positiveness, thereby eliminating the irrationality of the model in that paper.…”

“…The main contributions of this paper include: (1) We adopt a state-dependent risk aversion parameter, which is a linear function of the current wealth level after contribution, to describe the investor's risk attitude and investigate the multi-period mean-variance optimization problem for a DC pension plan. (2) We modify the wealth process to ensure its positiveness, thus, eliminating the irrational case of the model that appeared in Wang and Chen [14]. 3We obtain the closed-form equilibrium control for our problem, where the investment in the risky asset takes a linear feedback form of the current wealth level and the current contribution level.…”