Dynkin games in a general framework

Magdalena Kobylanski (1) , Marie-Claire Quenez (2, 3) , Marc Roger de Campagnolle (2)

1 LAMA - Laboratoire d'Analyse et de Mathématiques Appliquées
2 LPMA - Laboratoire de Probabilités et Modèles Aléatoires
3 MATHFI - Financial mathematics

We revisit the Dynkin game problem in a general framework and relax some assumptions. The payoffs and the criterion are expressed in terms of families of random variables indexed by stopping times. We construct two nonnegative supermartingales families $J$ and $J'$ whose finitness is equivalent to the Mokobodski's condition. Under some weak right-regularity assumption on the payoff families, the game is shown to be fair and $J-J'$ is shown to be the common value function. Existence of saddle points is derived under some weak additional assumptions. All the results are written in terms of random variables and are proven by using only classical results of probability theory.

Mots clés: Dynkin Games; Optimal stopping; Martingale methods

Domaines: Probabilités [math.PR]

Magdalena Kobylanski, Marie-Claire Quenez, Marc Roger de Campagnolle. Dynkin games in a general framework. 2011. ⟨hal-00795370v2⟩