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We consider the life-cycle optimal portfolio choice problem faced by an agentreceiving labor income and allocating her wealth to risky assets and a risklessbond subject to a borrowing constraint. In this paper, to reflect a realisticeconomic setting, we propose a model where the dynamics of the labor income hastwo main features. First, labor income adjust slowly to financial marketshocks, a feature already considered in Biffis, E., Gozzi, F. and Prosdocimi,C. (2020) - "Optimal portfolio choice with path dependent labor income: theinfinite horizon case". Second, the labor income $y_i$ of an agent $i$ isbenchmarked 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 facedtaking the limit when $n\to +\infty$ so that the problem falls into the familyof optimal control of infinite dimensional McKean-Vlasov Dynamics, which is acompletely new and challenging research field. We study the problem in asimplified case where, adding a suitable new variable, we are able to findexplicitly the solution of the associated HJB equation and find the optimalfeedback controls.

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