Stochastic Maximum Principle for Forward-Backward Regime Switching Jump Diffusion Systems and Applications to Finance

Citation:

Siyu LV,Zhen WU.Stochastic Maximum Principle for Forward-Backward Regime Switching Jump Diffusion Systems and Applications to Finance[J].Chinese Annals of Mathematics B,2018,39(5):773~790
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Authors:

Siyu LV; Zhen WU

Foundation:

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.
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.

Keywords:

Stochastic maximum principle, Dynamic programming principle,Forward-backward stochastic differential equation,Regime switching, Jump diffusion

Classification:

93E20, 60H10, 91B26
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