scholarly journals Infinite Horizon Stochastic Impulse Control with Delay and Random Coefficients

2021 ◽  
Author(s):  
Boualem Djehiche ◽  
Said Hamadène ◽  
Ibtissem Hdhiri ◽  
Helmi Zaatra
Keyword(s):  
Stochastic Process ◽  
Optimal Strategy ◽  
Impulse Control ◽  
Infinite Horizon ◽  
Random Coefficients ◽  
Control Problems ◽  
Snell Envelope ◽  
Stochastic Impulse Control ◽  
Admissible Strategies ◽  
Execution Delay

We study a class of infinite horizon impulse control problems with execution delay when the dynamics of the system is described by a general stochastic process adapted to the Brownian filtration. The problem is solved by means of probabilistic tools relying on the notion of Snell envelope and infinite horizon reflected backward stochastic differential equations. This allows us to establish the existence of an optimal strategy over all admissible strategies.

A General Verification Result for Stochastic Impulse Control Problems

2017 ◽  
Vol 55 (2) ◽  
pp. 627-649 ◽  
Author(s):  
Christoph Belak ◽  
Sören Christensen ◽  
Frank Thomas Seifried
Keyword(s):  
Impulse Control ◽  
Control Problems ◽  
Stochastic Impulse Control

scholarly journals Infinite horizon impulse control problem with jumps and continuous switching costs

2021 ◽  
Vol ahead-of-print (ahead-of-print) ◽  
Author(s):  
Rim Amami ◽  
Monique Pontier ◽  
Hani Abidi
Keyword(s):  
Differential Equations ◽  
Control Problem ◽  
Stochastic Differential Equations ◽  
Optimal Strategy ◽  
Impulse Control ◽  
Backward Stochastic Differential Equation ◽  
Infinite Horizon ◽  
Backward Stochastic Differential Equations ◽  
Content Type ◽  
Impulse Control Problem

PurposeThe purpose of this paper is to show the existence results for adapted solutions of infinite horizon doubly reflected backward stochastic differential equations with jumps. These results are applied to get the existence of an optimal impulse control strategy for an infinite horizon impulse control problem.Design/methodology/approachThe main methods used to achieve the objectives of this paper are the properties of the Snell envelope which reduce the problem of impulse control to the existence of a pair of right continuous left limited processes. Some numerical results are provided to show the main results.FindingsIn this paper, the authors found the existence of a couple of processes via the notion of doubly reflected backward stochastic differential equation to prove the existence of an optimal strategy which maximizes the expected profit of a firm in an infinite horizon problem with jumps.Originality/valueIn this paper, the authors found new tools in stochastic analysis. They extend to the infinite horizon case the results of doubly reflected backward stochastic differential equations with jumps. Then the authors prove the existence of processes using Envelope Snell to find an optimal strategy of our control problem.

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