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Article Dans Une Revue The Annals of Applied Probability Année : 2015

Randomized and backward SDE representation for optimal control of non-Markovian SDEs

Résumé

We study optimal stochastic control problems for non-Markovian stochastic differential equations (SDEs) where the drift, diffusion coefficients and gain functionals are path-dependent, and importantly we do not make any ellipticity assumptions on the SDE. We develop a control randomization approach and prove that the value function can be reformulated under a family of dominated measures on an enlarged filtered probability space. This value function is then characterized by a backward SDE with nonpositive jumps under a single probability measure, which can be viewed as a path-dependent version of the Hamilton Jacobi Bellman equation, and an extension to G-expectation.

Dates et versions

hal-01172283 , version 1 (07-07-2015)

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M. Fuhrman, H. Pham. Randomized and backward SDE representation for optimal control of non-Markovian SDEs. The Annals of Applied Probability, 2015, 25 (4), pp.2134-2167. ⟨10.1214/14-AAP1045⟩. ⟨hal-01172283⟩
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