Open this publication in new window or tab >>2022 (English)In: Stochastic Processes and their Applications, ISSN 0304-4149, E-ISSN 1879-209X, Vol. 145, p. 48-85Article in journal (Refereed) Published
Abstract [en]
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 gamma i of an agent i is benchmarked against the labor incomes of a population gamma(n) := (gamma(1),gamma(2)<b>, ...,gamma(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 -> +infinity 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). (C) 2021 Elsevier B.V. All rights reserved.
Place, publisher, year, edition, pages
Elsevier BV, 2022
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
National Category
Probability Theory and Statistics
Identifiers
urn:nbn:se:kth:diva-312694 (URN)10.1016/j.spa.2021.11.010 (DOI)000789706700003 ()2-s2.0-85121449800 (Scopus ID)
Note
QC 20220524
2022-05-242022-05-242022-06-25Bibliographically approved