Wage Rigidity and Retirement in Optimal Portfolio Choice

27 Pages Posted: 5 Mar 2021 Last revised: 8 Jan 2024

See all articles by Sara Biagini

Sara Biagini

LUISS University

Enrico Biffis

Imperial College Business School

Fausto Gozzi

Luiss

Margherita Zanella

Luiss Guido Carli University

Date Written: December 31, 2023

Abstract

We study an agent’s lifecycle portfolio choice problem with stochastic labor income, borrowing constraints and a finite retirement date. Similarly to [7], 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 delicate due 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. As opposed to models with Markovian dynamics, path dependency can now modulate the hedging demand arising from the implicit holding of risky assets in human capital, leading to richer asset allocation predictions consistent with wage rigidity and agents learning about their earning potential.

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

Biagini, Sara and Biffis, Enrico and Gozzi, Fausto and Zanella, Margherita, Wage Rigidity and Retirement in Optimal Portfolio Choice (December 31, 2023). Available at SSRN: https://ssrn.com/abstract=3772244 or http://dx.doi.org/10.2139/ssrn.3772244

Sara Biagini

LUISS University ( email )

Viale Romania 32
Rome, 00197
Italy

Enrico Biffis

Imperial College Business School ( email )

Imperial College London
South Kensington campus
London, SW7 2AZ
United Kingdom

Fausto Gozzi (Contact Author)

Luiss ( email )

Viale di Villa Massimo, 57
Rome, 00161
Italy

HOME PAGE: http://www.luiss.it/docenti/curricula/index.php?cod=Z08

Margherita Zanella

Luiss Guido Carli University ( email )

Via O. Tommasini 1
Rome, Roma 00100
Italy

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