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

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 l...

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Bibliographic Details
Published in:Stochastic processes and their applications Vol. 145; pp. 48 - 85
Main Authors: Djehiche, Boualem, Gozzi, Fausto, Zanco, Giovanni, Zanella, Margherita
Format: Journal Article
Language:English
Published: Elsevier B.V 01.03.2022
Subjects:
Dynamic programming/optimal control of SDEs in infinite dimension with Mc Kean-Vlasov dynamics and state constraints
Life-cycle optimal portfolio with labor income following path dependent and law dependent dynamics
Second order Hamilton-Jacobi-Bellman equations in infinite dimension
Verification theorems and optimal feedback controls
34K50
93E20
49L20
91G10
Life-cycle optimal portfolio with labor income following path dependent and law dependent dynamics
Verification theorems and optimal feedback controls
49N80
35Q89
35R15
Dynamic programming/optimal control of SDEs in infinite dimension with Mc Kean–Vlasov dynamics and state constraints
91G80
Second order Hamilton–Jacobi–Bellman equations in infinite dimension
ISSN:0304-4149, 1879-209X, 1879-209X
Online Access:Get full text
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Summary: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. 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. The techniques are a careful and nontrivial extension of the ones introduced in the previous papers of Biffis et al. (2015, 0000).
ISSN:0304-4149
1879-209X
1879-209X
DOI:10.1016/j.spa.2021.11.010