Optimal Portfolio, Consumption-Leisure and Retirement Choice Problem with Ces Utility

We study optimal portfolio, consumption-leisure and retirement choice of an infinitely-lived economic agent whose instantaneous preference is characterized by a constant elasticity of substitution(CES) function of consumption and leisure. We integrate in one model the optimal consumption-leisure-work choice, optimal portfolio selection, and the optimal stopping problem in which the agent chooses her retirement time. The economic agent derives utility from both consumption and leisure, and is able to adjust her supply of labor flexibly above a certain minimum work-hour, and also has a retirement option. We solve the problem analytically by considering a variational inequality arising from the dual functions of the optimal stopping problem. The optimal retirement time is characterized as the first time when her wealth exceeds a certain critical level. We provide the critical wealth level for retirement and characterize the optimal consumption-leisure and portfolio policy before and after retirement in closed forms. We also derive properties of the optimal policy. In particular, we show that consumption in general jumps around retirement. For the special case where the elasticity of substitution between consumption and leisure is equal to 1 we show that the option to retire reduces consumption and encourages risk taking