Optimal consumption-leisure, portfolio and retirement selection based on α-maxmin expected CES utility with ambiguity

Abstract

This article studies optimal consumption-leisure, portfolio and retirement selection of an infinitely lived investor whose preference is formulated by α-maxmin expected CES utility which is to differentiate ambiguity and ambiguity attitude. Adopting the recursive multiplepriors utility and the technique of backward stochastic differential equations (BSDEs), we transform the α-maxmin expected CES utility into a classical expected CES utility under a new probability measure related to the degree of an investor’s uncertainty. Our model investigates the optimal consumption-leisure-work selection, the optimal portfolio selection, and the optimal stopping problem. In this model, the investor is able to adjust her supply of labor flexibly above a certain minimum work-hour along with a retirement option. The problem can be analytically solved by using a variational inequality. And the optimal retirement time is given as the first time when her wealth exceeds a certain critical level. The optimal consumption-leisure and portfolio strategies before and after retirement are provided in closed forms. Finally, the distinctions of optimal consumption-leisure, portfolio and critical wealth level under ambiguity from those with no vagueness are discussed.