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The Relationship between the Stochastic Maximum Principle and the Dynamic Programming in Singular Control of Jump Diffusions
Joint Authors
Mezerdi, Brahim
Chighoub, Farid
Source
International Journal of Stochastic Analysis
Issue
Vol. 2014, Issue 2014 (31 Dec. 2014), pp.1-17, 17 p.
Publisher
Hindawi Publishing Corporation
Publication Date
2014-01-09
Country of Publication
Egypt
No. of Pages
17
Main Subjects
Abstract EN
The main objective of this paper is to explore the relationship between the stochastic maximum principle (SMP in short) and dynamic programming principle (DPP in short), for singular control problems of jump diffusions.
First, we establish necessary as well as sufficient conditions for optimality by using the stochastic calculus of jump diffusions and some properties of singular controls.
Then, we give, under smoothness conditions, a useful verification theorem and we show that the solution of the adjoint equation coincides with the spatial gradient of the value function, evaluated along the optimal trajectory of the state equation.
Finally, using these theoretical results, we solve explicitly an example, on optimal harvesting strategy, for a geometric Brownian motion with jumps.
American Psychological Association (APA)
Chighoub, Farid& Mezerdi, Brahim. 2014. The Relationship between the Stochastic Maximum Principle and the Dynamic Programming in Singular Control of Jump Diffusions. International Journal of Stochastic Analysis،Vol. 2014, no. 2014, pp.1-17.
https://search.emarefa.net/detail/BIM-453986
Modern Language Association (MLA)
Chighoub, Farid& Mezerdi, Brahim. The Relationship between the Stochastic Maximum Principle and the Dynamic Programming in Singular Control of Jump Diffusions. International Journal of Stochastic Analysis No. 2014 (2014), pp.1-17.
https://search.emarefa.net/detail/BIM-453986
American Medical Association (AMA)
Chighoub, Farid& Mezerdi, Brahim. The Relationship between the Stochastic Maximum Principle and the Dynamic Programming in Singular Control of Jump Diffusions. International Journal of Stochastic Analysis. 2014. Vol. 2014, no. 2014, pp.1-17.
https://search.emarefa.net/detail/BIM-453986
Data Type
Journal Articles
Language
English
Notes
Includes bibliographical references
Record ID
BIM-453986