The Relationship between the Stochastic Maximum Principle and the Dynamic Programming in Singular Control of Jump Diffusions | Zendy

Farid Chighoub | Zendy; Brahim Mezerdi | Zendy

Open Access

The Relationship between the Stochastic Maximum Principle and the Dynamic Programming in Singular Control of Jump Diffusions

Author(s) -

Farid Chighoub,

Brahim Mezerdi

Publication year - 2014

Publication title -

international journal of stochastic analysis

Language(s) - English

Resource type - Journals

SCImago Journal Rank - 0.19

H-Index - 28

eISSN - 2090-3340

pISSN - 2090-3332

DOI - 10.1155/2014/201491

Subject(s) - mathematics , maximum principle , smoothness , jump , optimal control , brownian motion , singular control , bellman equation , dynamic programming , jump diffusion , stochastic control , mathematical analysis , mathematical optimization , statistics , physics , quantum mechanics

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 usingthe 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

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