Numerical methods for an optimal multiple stopping problem

Imène Ben Latifa (1) , Joseph Fréderic Bonnans (2, 3) , Mohamed Mnif (1)

1 LR-LAMSIN-ENIT - Laboratoire de Modélisation Mathématique et Numérique dans les Sciences de l'Ingénieur [Tunis]
2 CMAP - Centre de Mathématiques Appliquées - Ecole Polytechnique
3 Commands - Control, Optimization, Models, Methods and Applications for Nonlinear Dynamical Systems

This paper deals with numerical solutions to an optimal multiple stopping problem. The corresponding dynamic programing (DP) equation is a variational inequality satisfied by the value function in the viscosity sense. The convergence of the numerical scheme is shown by viscosity arguments. An optimal quantization method is used for computing the conditional expectations arising in the DP equation. Numerical results are presented for the price of swing option and the behavior of the value function.

Mots clés: Quantization; swing option; optimal multiple stopping time problem.

Domaines: Probabilités [math.PR]; Optimisation et contrôle [math.OC]

Imène Ben Latifa, Joseph Fréderic Bonnans, Mohamed Mnif. Numerical methods for an optimal multiple stopping problem. Stochastics and Dynamics, 2016, 16 (4), pp.27. ⟨10.1142/S0219493716500167⟩. ⟨hal-01248282⟩