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

Bernt Øksendal (1) , Agnès Sulem (2) , Tusheng Zhang (3)

1 CMA - Center of Mathematics for Applications [Oslo]
2 MATHRISK - Mathematical Risk handling
3 School of Mathematics - Department of Mathematics [Manchester]

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.

Domaines: Mathématiques générales [math.GM]

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