Affiliation:
1. Laboratory of Applied Mathematics, University Mohamed Khider, P.O. Box 145, 07000 Biskra, Algeria
Abstract
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.
Funder
Générale de la Recherche Scientifique et du Développement Technologique, Algeria
Subject
Applied Mathematics,Modeling and Simulation,Statistics and Probability,Analysis
Cited by
3 articles.
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