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

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 repr...

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Bibliographic Details
Published inJournal of optimization theory and applications Vol. 179; no. 2; pp. 696 - 721
Main Authors Savku, Emel, Weber, Gerhard-Wilhelm
Format Journal Article
LanguageEnglish
Published New York Springer US 01.11.2018
Springer Nature B.V
Subjects
Applications of Mathematics
Calculus of Variations and Optimal Control; Optimization
Delay
Differential equations
Economic models
Engineering
Existence theorems
Markov chains
Mathematics
Mathematics and Statistics
Maximum principle
Operations Research/Decision Theory
Optimal control
Optimization
Stochastic models
Switching
Theory of Computation
Uniqueness theorems
60J75
Stochastic delay equations
93E20
Regime switching
Anticipated backward stochastic differential equations
Optimal consumption
Jump-diffusions
91G80
Stochastic maximum principle
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Summary: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.
Bibliography:ObjectType-Article-1
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ISSN:0022-3239
1573-2878
DOI:10.1007/s10957-017-1159-3