Abstract
The authors prove a sufficient stochastic maximum principle for the optimal control of a forward-backward Markov regime switching jump diffusion system and show its connection to dynamic programming principle. The result is applied to a cash flow valuation problem with terminal wealth constraint in a financial market. An explicit optimal strategy is obtained in this example.
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The authors would like to thank the anonymous referee for valuable comments, which led to a much better version of this paper.
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This work was supported by the National Natural Science Foundation of China (No. 61573217), the 111 Project (No.B12023), the National High-level Personnel of Special Support Program and the Chang Jiang Scholar Program of the Ministry of Education of China.
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Lv, S., Wu, Z. Stochastic Maximum Principle for Forward-Backward Regime Switching Jump Diffusion Systems and Applications to Finance. Chin. Ann. Math. Ser. B 39, 773–790 (2018). https://doi.org/10.1007/s11401-018-0095-3
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DOI: https://doi.org/10.1007/s11401-018-0095-3
Keywords
- Stochastic maximum principle
- Dynamic programming principle
- Forward-backward stochastic differential equation
- Regime switching
- Jump diffusion