Numerical approximation for an impulse control problem arising in portfolio selection under liquidity risk

Vathana Ly Vath (1) , Mohamed Mnif (2)

1 LPMA - Laboratoire de Probabilités et Modèles Aléatoires
2 LR-LAMSIN-ENIT - Laboratoire de Modélisation Mathématique et Numérique dans les Sciences de l'Ingénieur [Tunis]

We investigate numerical aspects of a portfolio selection problem studied in [10], in which we suggest a model of liquidity risk and price impact and formulate the problem as an impulse control problem under state constraint. We show that our impulse control problem could be reduced to an iterative sequence of optimal stopping problems. Given the dimension of our problem and the complexity of its solvency region, we use Monte Carlo methods instead of finite difference methods to calculate the value function, the transaction and no-transaction regions. We provide a numerical approximation algorithm as well as numerical results for the optimal transaction strategy.

Keywords: Impulse control problem; Optimal transaction strategy; Monte Carlo method; Malliavin calculus.; Malliavin calculus

Domains: Probability [math.PR]

Vathana Ly Vath, Mohamed Mnif. Numerical approximation for an impulse control problem arising in portfolio selection under liquidity risk. 2007. ⟨hal-00135815⟩