Optimal Portfolio Choice With Path-Dependent Labor Income: Finite Retirement Time

26 Pages Posted: 5 Mar 2021

See all articles by Enrico Biffis

Enrico Biffis

Imperial College Business School

Gianluca Cappa

affiliation not provided to SSRN

Fausto Gozzi

Luiss

Margherita Zanella

Luiss Guido Carli University

Date Written: January 23, 2021

Abstract

This paper extends the project initiated in and studies a lifecycle portfolio choice problem with borrowing constraints and finite retirement time in which an agent receives labor income that adjusts to financial market shocks in a path dependent way. The novelty here, with respect to, is the fact that we have a finite retirement time, which makes the model more realistic, but harder to solve. The presence of both path-dependency, as in, and finite retirement, leads to a two-stage infinite dimensional stochastic optimal control problem, a family of problems which, to our knowledge, has not yet been treated in the literature. We solve the problem completely, and find explicitly the optimal controls in feedback form. This is possible because we are able to find an explicit solution to the associated infinite dimensional Hamilton-Jacobi-Bellman (HJB) equation, even if state constraints are present. Note that, differently from, here the HJB equation is of parabolic type, hence the work to identify the solutions and optimal feedbacks is more delicate, as it involves, in particular, time-dependent state constraints, which, as far as we know, have not yet been treated in the infinite dimensional literature. The explicit solution allows us to study the properties of optimal strategies and discuss their financial implications.

Suggested Citation

Biffis, Enrico and Cappa, Gianluca and Gozzi, Fausto and Zanella, Margherita, Optimal Portfolio Choice With Path-Dependent Labor Income: Finite Retirement Time (January 23, 2021). Available at SSRN: https://ssrn.com/abstract=3772244 or http://dx.doi.org/10.2139/ssrn.3772244

Enrico Biffis

Imperial College Business School ( email )

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

Gianluca Cappa

affiliation not provided to SSRN

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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