Mixed generalized Dynkin game and stochastic control in a Markovian framework
Dumitrescu, Roxana; Quenez, Marie-Claire; Sulem, Agnès (2016), Mixed generalized Dynkin game and stochastic control in a Markovian framework, Stochastics, 89, 1, p. 400-429. 10.1080/17442508.2016.1230614
TypeArticle accepté pour publication ou publié
Taylor & Francis
MetadataShow full item record
CEntre de REcherches en MAthématiques de la DEcision [CEREMADE]
Laboratoire de Probabilités et Modèles Aléatoires [LPMA]
Abstract (EN)We introduce a mixed generalized Dynkin game/stochastic control with E f-expectation in a Markovian framework. We study both the case when the terminal reward function is Borelian only and when it is continuous. By using the characterization of the value function of a generalized Dynkin game via an associated doubly reflected BSDEs (DRBSDE) first provided in [16 ], we obtain that the value function of our problem coincides with the value functionof an optimization problem for DRBSDEs. Using this property, we establish a weak dynamic programming principle by extending some results recently provided in [17 ]. We then show a strong dynamic programming principle in the continuous case, which cannot be derived from the weak one. In particular, we have to prove that the value function of the problem is continuous with respect to time t, which requires some technical tools of stochastic analysis and new results on DRBSDEs. We finally study the links between our mixed problem and generalized Hamilton–Jacobi–Bellman variational inequalities in both cases.
Subjects / KeywordsGeneralized Dynkin games; Markovian stochastic control; mixed stochastic control/Dynkin game with nonlinear expectation; doubly reflected BSDEs; dynamic programming principles; generalized Hamilton–Jacobi–Bellman variational inequalities; viscosity solution
Showing items related by title and author.
A Weak Dynamic Programming Principle for Combined Optimal Stopping / Stochastic Control with Ef -conditional Expectations Dumitrescu, Roxana; Quenez, Marie-Claire; Sulem, Agnès (2016) Article accepté pour publication ou publié