scholarly journals A General Stochastic Maximum Principle for Singular Control Problems

2005 ◽  
Vol 10 (0) ◽  
pp. 988-1004 ◽  
Author(s):  
Seid Bahlali ◽  
Brahim Mezerdi
Keyword(s):  
Maximum Principle ◽  
Singular Control ◽  
Stochastic Maximum Principle ◽  
Control Problems ◽  
General Stochastic

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

2014 ◽  
Vol 2014 ◽  
pp. 1-17 ◽  
Author(s):  
Farid Chighoub ◽  
Brahim Mezerdi
Keyword(s):  
Dynamic Programming ◽  
Maximum Principle ◽  
Sufficient Conditions ◽  
Singular Control ◽  
Stochastic Maximum Principle ◽  
Dynamic Programming Principle ◽  
Optimal Harvesting ◽  
Spatial Gradient ◽  
Jump Diffusions ◽  
The Relationship

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.

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