Optimal Portfolio Choice with Path Dependent Labor Income: The Infinite Horizon Case

32 Pages Posted: 29 May 2019 Last revised: 2 Feb 2020

See all articles by Enrico Biffis

Enrico Biffis

Imperial College Business School

Fausto Gozzi

Luiss

Cecilia Prosdocimi

Luiss Guido Carli University

Date Written: January 31, 2020

Abstract

We consider an infinite horizon portfolio problem with borrowing constraints, in which an agent receives labor income which adjusts to financial market shocks in a path dependent way. This path-dependency is the novelty of the model, and leads to an infinite dimensional stochastic optimal control problem. 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. To the best of our knowledge, this is the first infinite dimensional generalization of Merton's optimal portfolio problem for which explicit solutions can be found. The explicit solution allows us to study the properties of optimal strategies and discuss their financial implications.

Keywords: optimal portfolio choice, stochastic delay differential equations, labor income, human capital, hedging demand

JEL Classification: G11, G13

Suggested Citation

Biffis, Enrico and Gozzi, Fausto and Prosdocimi, Cecilia, Optimal Portfolio Choice with Path Dependent Labor Income: The Infinite Horizon Case (January 31, 2020). Available at SSRN: https://ssrn.com/abstract=3381508 or http://dx.doi.org/10.2139/ssrn.3381508

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

Cecilia Prosdocimi

Luiss Guido Carli University ( email )

Via O. Tommasini 1
Rome, Roma 00100
Italy

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