Feynman-Kac representation for Hamilton-Jacobi-Bellman IPDE
By Idris Kharroubi, Huyen Pham. 2012
70 citations recorded by the source corpus.
We aim to provide a Feynman-Kac type representation for Hamilton-Jacobi-Bellman equation, in terms of Forward Backward Stochastic Differential Equation (FBSDE) with a simulatable forward process. For this purpose, we introduce a class of BSDE where the jumps component of the solution is subject to a partial nonpositive constraint. Existence and approximation of a unique minimal solution is proved by a penalization method under mild assumptions. We then show how minimal solution to this BSDE class provides a new probabilistic representation for nonlinear integro-partial differential equations (IPDEs) of Hamilton-Jacobi-Bellman (HJB) type, when considering a regime switching forward SDE in a Markovian framework. Moreover, we state a dual formula of this BSDE minimal solution involving equivalent change of probability measures. This gives in particular an original representation for value functions of stochastic control problems including controlled diffusion coefficient.
Subfields: Demography, Finance
View Paper: https://www.semanticscholar.org/paper/d501d999d4e506e5153b125566168a5055c4ef25
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In Demography
- Andrea Cosso
- Erhan Bayraktar
- Huyen Pham
- Yasushi Ishikawa
- Marek Musiela
- Thaleia Zariphopoulou
- Kenneth Hvistendahl Karlsen
- Fred Espen Benth
In Finance
- Andrea Cosso
- Huyen Pham
- Erhan Bayraktar
- Thaleia Zariphopoulou
- Jianfeng Zhang
- P. J. Graber
- Yasushi Ishikawa
- Peter A. Forsyth
Citations in the corpus
- Randomized dynamic programming principle and Feynman-Kac representation for optimal control of McKean-Vlasov dynamics (2016, methodology): “2 D On a different randomization of the control In the present appendix we introduce, following [19], a different kind of randomization, which in our paper turns out to be useful in the proof of Theorem 4.”