Optimal stopping and stochastic control differential games for jump diffusions

Fouzia Baghery (1) , Sven Haadem (2) , Bernt Oksendal (2) , Isabelle Turpin (1)

1 LAMAV - Laboratoire de Mathématiques et leurs Applications de Valenciennes - EA 4015
2 UiO - University of Oslo

We study stochastic differential games of jump diffusions driven by Brownian motions and compensated Poisson random measures, where one of the players can choose the stochastic control and the other player can decide when to stop the system. We prove a verification theorem for such games in terms of a HamiltonJacobiBellman variational inequality. The results are applied to study some specific examples, including optimal resource extraction in a worst-case scenario, and risk minimizing optimal portfolio and stopping.

Mots clés: optimal stopping; stochastic control; stochastic differential games; jump diffusions; optimal resource extraction in a worst-case scenario; risk minimizing portfolios

Domaines: Mathématiques [math]

Fouzia Baghery, Sven Haadem, Bernt Oksendal, Isabelle Turpin. Optimal stopping and stochastic control differential games for jump diffusions. Stochastics: An International Journal of Probability and Stochastic Processes, 2013, 85 (1), pp.85-97. ⟨10.1080/17442508.2011.652116⟩. ⟨hal-03149926⟩