# A Viscosity Approach to Stochastic Differential Games of Control and Stopping Involving Impulsive Control

arXiv: https://arxiv.org/abs/1803.11432 · HTML: https://mlsanity.com/paper/1803.11432/

## Key facts

- Cited by 5 papers in the map (data through 14 Oct 2026).
- First posted on arXiv 30 Mar 2018.

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## Abstract (arXiv)

This paper analyses a stochastic differential game of control and stopping in which one of the players modifies a diffusion process using impulse controls, an adversary then chooses a stopping time to end the game. The paper firstly establishes the regularity and boundedness of the upper and lower value functions from which an appropriate variant of the dynamic programming principle (DPP) is derived. It is then proven that the upper and lower value functions coincide so that the game admits a value and that the value of the game is a unique viscosity solution to a HJBI equation described by a double obstacle quasi-integro-variational inequality.