A Stochastic Maximum Principle for a Markov Regime-Switching Jump-Diffusion Model with Delay and an Application to Finance

Date

2018-11-01

Author

Savku, Emel
Weber, Gerhard Wilhelm

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We study a stochastic optimal control problem for a delayed Markov regime-switching jump-diffusion model. We establish necessary and sufficient maximum principles under full and partial information for such a system. We prove the existence-uniqueness theorem for the adjoint equations, which are represented by an anticipated backward stochastic differential equation with jumps and regimes. We illustrate our results by a problem of optimal consumption problem from a cash flow with delay and regimes.

Subject Keywords

Stochastic maximum principle, Regime switching, Stochastic delay equations, Anticipated backward stochastic differential equations, Jump-diffusions, Optimal consumption, 93E20, 91G80, 60J75

URI

https://hdl.handle.net/11511/57917

Journal

JOURNAL OF OPTIMIZATION THEORY AND APPLICATIONS

DOI

https://doi.org/10.1007/s10957-017-1159-3

Collections

Graduate School of Applied Mathematics, Article

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Citation Formats

E. Savku and G. W. Weber, “A Stochastic Maximum Principle for a Markov Regime-Switching Jump-Diffusion Model with Delay and an Application to Finance,” JOURNAL OF OPTIMIZATION THEORY AND APPLICATIONS, pp. 696–721, 2018, Accessed: 00, 2020. [Online]. Available: https://hdl.handle.net/11511/57917.