On Some Impulse Control Problems with Constraint

The impulse control of a Markov--Feller process is considered when the impulses are allowed only when a signal arrives. This is referred to as an impulse control problem with constraint. A detailed setting is described, a characterization of the optimal cost is obtained using previous results of the authors on optimal stopping problems with constraint, and an optimal impulse control is identified.

[1]  Jukka Lempa.  Optimal Stopping with Information Constraint , 2012 .

[2]  J. Menaldi.  Optimal impulse control problems for degenerate diffusions with jumps , 1987 .

[3]  O. Hernández-Lerma,et al.  Further topics on discrete-time Markov control processes , 1999 .

[4]  Paul Dupuis,et al.  Optimal stopping with random intervention times , 2002, Advances in Applied Probability.

[5]  Alain Bensoussan,et al.  Applications des Inequations Varia-tionnelles en Controle Stochastique , 1978 .

[6]  R. Seydel.  Existence and uniqueness of viscosity solutions for QVI associated with impulse control of jump-diffusions , 2009 .

[7]  Alʹbert Nikolaevich Shiri︠a︡ev,et al.  Optimal Stopping and Free-Boundary Problems , 2006 .

[8]  Impulse control of stochastic Navier – Stokes equations , 2002 .

[9]  A. Bensoussan,et al.  Contrôle impulsionnel et inéquations quasi variationnelles , 1982 .

[10]  A. Bensoussan.  Stochastic control by functional analysis methods , 1982 .

[11]  B. Marchal,et al.  Theorie Generale du Controle Impulsionnel Markovien , 1984 .

[12]  Hui Wang,et al.  Some control problems with random intervention times , 2001, Advances in Applied Probability.

[13]  M. Robin,et al.  Contrôle impulsionnel des processus de Markov , 1978 .

[14]  Gechun Liang.  Stochastic Control Representations for Penalized Backward Stochastic Differential Equations , 2015, SIAM J. Control. Optim..

[15]  Mark H. Davis.  Markov Models and Optimization , 1995 .

[16]  Alain Bensoussan.  Dynamic Programming and Inventory Control , 2011 .

[17]  Maurice Robin,et al.  On Some Optimal Stopping Problems with Constraint , 2016, SIAM J. Control. Optim..

[18]  Gechun Liang,et al.  Optimal Switching at Poisson Random Intervention Times , 2013, 1309.5608.