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...

Celý popis

Uložené v:

Podrobná bibliografia
Vydané v:	Stochastic processes and their applications Ročník 145; s. 48 - 85
Hlavní autori:	Djehiche, Boualem, Gozzi, Fausto, Zanco, Giovanni, Zanella, Margherita
Médium:	Journal Article
Jazyk:	English
Vydavateľské údaje:	Elsevier B.V 01.03.2022
Predmet:	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
On-line prístup:	Získať plný text
Tagy:	Pridať tag Žiadne tagy, Buďte prvý, kto otaguje tento záznam!

Popis
Shrnutí:	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