Optimal stopping for Lévy processes and affine functions

Diana Dorobantu (1)

1 LSP - Laboratoire de Statistique et Probabilités

This paper studies an optimal stopping problem for Lévy processes. We give a justification of the form of the Snell envelope using standard results of optimal stopping. We also justify the convexity of the value function, and without a priori restriction to a particular class of stopping times, we deduce that the smallest optimal stopping time is necessarily a hitting time. We propose a method which allows to obtain the optimal threshold. Moreover this method allows to avoid long calculations of the integro-differential operatorused in the usual proofs.

Mots clés: Lévy processes; optimal stopping problem; hitting time; Snell envelope.; Snell envelope

Domaines: Probabilités [math.PR]

Diana Dorobantu. Optimal stopping for Lévy processes and affine functions. 2008. ⟨hal-00274545⟩