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

Boualem Djehiche, Fausto Gozzi, Giovanni Zanco and Margherita Zanella

Stochastic Processes and their Applications, 2022, vol. 145, issue C, 48-85

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 adjusts slowly to financial market shocks, a feature already considered in Biffis et al. (2015). Second, the labor income yi of an agent i is benchmarked against the labor incomes of a population yn≔(y1,y2,…,yn) 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→+∞ 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.

Keywords: Life-cycle optimal portfolio with labor income following path dependent and law dependent dynamics; Dynamic programming/optimal control of SDEs in infinite dimension with Mc Kean–Vlasov dynamics and state constraints; Second order Hamilton–Jacobi–Bellman equations in infinite dimension; Verification theorems and optimal feedback controls (search for similar items in EconPapers)
Date: 2022
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Citations: View citations in EconPapers (4)

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DOI: 10.1016/j.spa.2021.11.010

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