A Stochastic HJB Equation for Optimal Control of Forward-Backward SDEs

Bernt Øksendal (), Agnès Sulem () and Tusheng Zhang ()
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Bernt Øksendal: University of Oslo, Blindern, Department of Mathematics
Agnès Sulem: University of Oslo, Blindern, Department of Mathematics
Tusheng Zhang: University of Manchester, School of Mathematics

A chapter in The Fascination of Probability, Statistics and their Applications, 2016, pp 435-446 from Springer

Abstract: Abstract We study optimal stochastic control problems of general coupled systems of forward-backward stochastic differential equations with jumps. By means of the Itô-Ventzell formula, the system is transformed into a controlled backward stochastic partial differential equation. Using a comparison principle for such equations we obtain a general stochastic Hamilton-Jacobi-Bellman (HJB) equation for the value function of the control problem. In the case of Markovian optimal control of jump diffusions, this equation reduces to the classical HJB equation. The results are applied to study risk minimization in financial markets.

Keywords: Stochastic control; Forward-backward SDEs; Stochastic HJB equation; Comparison principle; Portfolio optimization; Risk minimization (search for similar items in EconPapers)
Date: 2016
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Persistent link: https://EconPapers.repec.org/RePEc:spr:sprchp:978-3-319-25826-3_20

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DOI: 10.1007/978-3-319-25826-3_20

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