Optimal consumption policies in illiquid markets

H. Pham (1) , A. Cretarola , F. Gozzi , P. Tankov

1 LPMA - Laboratoire de Probabilités et Modèles Aléatoires

We investigate optimal consumption policies in the liquidity risk model introduced by Pham and Tankov (Math. Finance 18:613-627, 2008). Our main result is to derive smoothness C-1 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.

Domaines: Probabilités [math.PR]

H. Pham, A. Cretarola, F. Gozzi, P. Tankov. Optimal consumption policies in illiquid markets. Finance and Stochastics, 2011, 15 (1), pp.85-115. ⟨10.1007/s00780-010-0123-y⟩. ⟨hal-00564205⟩