A Weak Dynamic Programming Principle for Combined Optimal Stopping / Stochastic Control with Ef -conditional Expectations
Dumitrescu, Roxana; Quenez, Marie-Claire; Sulem, Agnès (2016), A Weak Dynamic Programming Principle for Combined Optimal Stopping / Stochastic Control with Ef -conditional Expectations, SIAM Journal on Control and Optimization, 54, 4, p. 2090-2015. 10.1137/15M1027012
TypeArticle accepté pour publication ou publié
Journal nameSIAM Journal on Control and Optimization
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CEntre de REcherches en MAthématiques de la DEcision [CEREMADE]
Laboratoire de Probabilités et Modèles Aléatoires [LPMA]
Abstract (EN)We study a combined optimal control/stopping problem under a nonlinear expectation Ef induced by a BSDE with jumps, in a Markovian framework. The terminal reward function is only supposed to be Borelian. The value function u associated with this problem is generally irregular. We first establish a sub- (resp. super-) optimality principle of dynamic programming involving its upper- (resp. lower-) semicontinuous envelope u∗ (resp. u∗). This result, called weak dynamic programming principle (DPP), extends that obtained in [ 8 ] in the case of a classical expectation to the case of an Ef-expectation and Borelian terminal reward function. Using this weak DPP, we then prove that u∗ (resp. u∗) is a viscosity sub- (resp. super-) solution of a nonlinear Hamilton-Jacobi-Bellman variational inequality.
Subjects / KeywordsHamilton-Jacobi-Bellman variational inequalities; Robust optimal stopping,; dynamic programming principle; viscosity solution; reflected backward stochastic differential equations with jumps; non linear expectation
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