Optimal portfolio choice with path dependent benchmarked labor income: a mean field model

TL;DR

This paper develops a novel mean field model for optimal portfolio choice that incorporates slow-adjusting, path-dependent labor income benchmarked against a large population, leading to explicit solutions for complex control problems.

Contribution

It introduces a new mean field framework for portfolio optimization with benchmarked, path-dependent labor income, solving the associated infinite-dimensional control problem explicitly.

Findings

Explicit solutions for the HJB equation in the mean field setting

Optimal feedback controls derived for the portfolio problem

Model captures realistic economic features like slow income adjustment and benchmarking

Abstract

We consider the life-cycle optimal portfolio choice problem faced by an agent receiving labor income and allocating her wealth to risky assets and a riskless bond subject to a borrowing constraint. In this paper, to reflect a realistic economic setting, we propose a model where the dynamics of the labor income has two main features. First, labor income adjust slowly to financial market shocks, a feature already considered in Biffis, E., Gozzi, F. and Prosdocimi, C. (2020) - "Optimal portfolio choice with path dependent labor income: the infinite horizon case". Second, the labor income $y_i$ of an agent $i$ is benchmarked against the labor incomes of a population $y^n:=(y_1,y_2,\ldots,y_n)$ of $n$ agents with comparable tasks and/or ranks. This last feature has not been considered yet in the literature and is faced taking the limit when $n\to +\infty$ so that the problem falls into the family of optimal control of infinite dimensional McKean-Vlasov Dynamics, which is a completely new and challenging research field. We study the problem in a simplified case where, adding a suitable new variable, we are able to find explicitly the solution of the associated HJB equation and find the optimal feedback controls.