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.
This research was carried out with support of CAS—Centre for Advanced Study, at the Norwegian Academy of Science and Letters, within the research program SEFE.
The research leading to these results has received funding from the European Research Council under the European Community’s Seventh Framework Programme (FP7/2007–2013)/ERC grant agreement no [228087].
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Øksendal, B., Sulem, A., Zhang, T. (2016). A Stochastic HJB Equation for Optimal Control of Forward-Backward SDEs. In: Podolskij, M., Stelzer, R., Thorbjørnsen, S., Veraart, A. (eds) The Fascination of Probability, Statistics and their Applications. Springer, Cham. https://doi.org/10.1007/978-3-319-25826-3_20
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DOI: https://doi.org/10.1007/978-3-319-25826-3_20
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