Equilibrium behavioral strategy for a DC pension plan with piecewise linear state-dependent risk tolerance

We investigate the equilibrium behavioral strategy for a defined contribution (DC) pension plan during the accumulation phase in this paper. We adopt a state-dependent function to describe the risk tolerance attitude of a mean-variance (MV) investor, which is a piecewise linear function of the current wealth level with the reference point being the discounted investment target. Meanwhile, the stochastic labor income is taken into account, whose risk sources arise from both financial and non-financial markets. The extended Hamilton-Jacobi-Bellman (HJB) system of equations for our problem is presented. Explicit expressions for the suboptimal equilibrium behavioral strategy and its corresponding equilibrium value function are obtained in the suboptimal sense by the stochastic control technique. We find that the suboptimal equilibrium behavioral strategy takes a piecewise linear feedback form of the current wealth level with respect to the discounted investment target, and it also depends on the current labor income. Finally, some numerical analyses are provided to illustrate the effects of model parameters on the suboptimal equilibrium behavioral strategy and the variance-expectation curve, which shed light on our theoretical results.