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A stochastic HJB equation for optimal control of forward-backward SDEs

Bernt Øksendal 1 Agnès Sulem 2 Tusheng Zhang 3 
2 MATHRISK - Mathematical Risk handling
Inria Paris-Rocquencourt, UPEM - Université Paris-Est Marne-la-Vallée, ENPC - École des Ponts ParisTech
Abstract : We study optimal stochastic control problems of general coupled systems of forward- backward stochastic di erential equations with jumps. By means of the It^o-Ventzell formula the system is transformed to a controlled backward stochastic partial di eren- tial equation (BSPDE) with jumps. Using a comparison principle for such BSPDEs we obtain a general stochastic Hamilton-Jacobi- Bellman (HJB) equation for such control problems. In the classical Markovian case with optimal control of jump di usions, the equation reduces to the classical HJB equation. The results are applied to study risk minimization in nancial markets.
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Submitted on : Monday, December 16, 2013 - 1:41:41 PM
Last modification on : Thursday, January 20, 2022 - 5:29:30 PM
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  • HAL Id : hal-00919141, version 1



Bernt Øksendal, Agnès Sulem, Tusheng Zhang. A stochastic HJB equation for optimal control of forward-backward SDEs. 2013. ⟨hal-00919141⟩



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