Optimal consumption policies in illiquid markets

Alessandra Cretarola (1) , Fausto Gozzi (1) , Huyên Pham (2, 3) , Peter Tankov (2)

1 Dipartimento di Scienze Economiche e Aziendali
2 LPMA - Laboratoire de Probabilités et Modèles Aléatoires
3 CREST - Centre de Recherche en Économie et Statistique

We investigate optimal consumption policies in the liquidity risk model introduced in Pham and Tankov (2007). Our main result is to derive smoothness results for the value functions of the portfolio/consumption choice problem. As an important consequence, we can prove the existence of the optimal control (portfolio/consumption strategy) which we characterize both in feedback form in terms of the derivatives of the value functions and as the solution of a second-order ODE. Finally, numerical illustrations of the behavior of optimal consumption strategies between two trading dates are given.

Keywords: Illiquid market; optimal consumption; integrodifferential equations; viscosity solutions; semiconcavity; sub(super) differentials; optimal control

Domains: Probability [math.PR]; Economics and Finance

Alessandra Cretarola, Fausto Gozzi, Huyên Pham, Peter Tankov. Optimal consumption policies in illiquid markets. 2008. ⟨hal-00292673⟩