Portfolio choice with illiquid asset for a loss-averse pension fund investor

This paper explores the optimization of liquid and illiquid assets investment for a defined contribution (DC) pension plan and investigates the impact of illiquidity on portfolio choice. In addition to three kinds of liquid assets, there is an illiquid asset that can only be traded at time 0, and it provides returns at retirement. The investor exhibits both risk-seeking and loss-averse behaviors, with S-shaped utility from the return on investment at retirement. In the long run, the investor also faces the risks caused by the time-varying income and inflation. The martingale method is adopted first to analyze the characteristics of the optimal investment strategy in a complete market. Then the optimal illiquid asset trading strategy is identified and determined. The results are proven to be applicable in a variety of market model settings through some extended analyses. Finally, several numerical findings are illustrated.