Wage Rigidity and Retirement in Optimal Portfolio Choice
30 Pages Posted: 5 Mar 2021 Last revised: 15 Sep 2022
Date Written: September 14, 2022
We study an agent’s lifecycle portfolio choice problem with stochastic labor income, borrowing constraints and a finite retirement date. Similarly to , wages evolve in a path-dependent way, but the presence of a finite retirement time leads to a novel, two-stage infinite dimensional stochastic optimal control problem, which we fully solve obtaining explicitly the optimal controls in feedback form. This is possible as we find an explicit solution to the associated Hamilton-Jacobi-Bellman (HJB) equation, which is an infinite dimensional PDE of parabolic type. The identification of the optimal feedbacks is more delicate than in  due to the two-stage structure and to the presence of time-dependent state constraints, which appear to be new in the infinite dimensional stochastic control literature. The explicit solution allows us to study the properties of optimal strategies and discuss their implications for portfolio choice. Importantly, we discuss not only the optimal allocations for the case of labor income spanned by the traded assets, but also provide novel insights into the case in which wages are also driven by idiosyncratic shocks.
Keywords: Stochastic delayed differential equations, infinite dimensional Merton problem with retirement, sticky wages, two-stage optimal control problems in infinite dimension with state constraints, second order parabolic Hamilton-Jacobi-Bellman equations in infinite dimension
JEL Classification: C32, D81, G11, G13, J30
Suggested Citation: Suggested Citation