Deterministic Minimax Impulse Control in Finite Horizon: the Viscosity Solution Approach

Abstract

We study here the impulse control minimax problem. We allow the cost functionals and dynamics to be unbounded and hence the value functions can possibly be unbounded. We prove that the value function of the problem is continuous. Moreover, the value function is characterized as the unique viscosity solution of an Isaacs quasi-variational inequality. This problem is in relation with an application in mathematical finance.

References in corpus (1)

• Optimal Multi-Modes Switching Problem in Infinite Horizon

Cited by in corpus (5)

• Feedback Nash Equilibria in Differential Games with Impulse Control
• Zero-sum stochastic differential game in finite horizon involving impulse controls
• Viscosity Solutions for a System of PDEs and Optimal Switching
• Continuous and Impulse Controls Differential Game in Finite Horizon with Nash-Equilibrium and Application
• Uniqueness of Viscosity Solutions for Optimal Multi-Modes Switching Problem with Risk of default