Optimal control of finite horizon type for a multidimensional delayed switching system

A Finite Horizon Optimal Multiple Switching Problem

We consider the problem of optimal multiple switching in finite horizon, when the state of the system, including the switching costs, is a general adapted stochastic process. The problem is formulated as an extended impulse control problem and completely solved using probabilistic tools such as the Snell envelop of processes and reflected backward stochastic differential equations. Finally, whe...

An Infinite Horizon Optimal Control Problem for Some Switching Systems

Solving finite time horizon Dynkin games by optimal switching

This paper uses recent results on continuous-time finite-horizon optimal switching problems with negative switching costs to prove the existence of a saddle point in an optimal stopping (Dynkin) game. Sufficient conditions for the game’s value to be continuous with respect to the time horizon are obtained using recent results on norm estimates for doubly reflected backward stochastic differenti...

Optimal Switching in Finite Horizon under State Constraints

We study an optimal switching problem with a state constraint: the controller is only allowed to choose strategies that keep the controlled diffusion in a closed domain. We prove that the value function associated with this problem is the limit of value functions associated with unconstrained switching problems with penalized coefficients, as the penalization parameter goes to infinity. This co...

Impulse Control of Multidimensional Jump Diffusions in Finite Time Horizon

This paper analyzes a class of impulse control problems for multidimensional jump diffusions in the finite time horizon. Following the basic mathematical setup from Stroock and Varadhan [Multidimensional Diffusion Processes, Springer-Verlag, Heidelberg, 2006], this paper first establishes rigorously an appropriate form of the dynamic programming principle. It then shows that the value function ...