Speaker：Jie Xiong (Southern University of Science and Technology)

Time：2023-5-5, 14:00-15:00

Location：Conference Room 105 at Experiment Building at Haiyun Campus

Abstract:

This talk is concerned with a two-player nonzero-sum stochastic differential game, where both players use impulse controls and the state process evolves as a regime switching diffusion. Based on a system of variational inequalities (VIs), a verification theorem as a sufficient criterion for optimality is established. Nash equilibrium strategies for the two players, indicating when and how it is optimal to intervene, are given in terms of the obstacle parts of the VIs. An important yet rather subtle issue is how to set an appropriate regularity condition for the solutions to the VIs, which together with the so-called smooth-fit principle lead to a suitable system of algebraic equations. As an application of the theoretical results, an example of exchange rate game between two countries is provided. By taking advantage of the verification theorem, a Nash equilibrium and the corresponding value functions are explicitly constructed. It is shown in this talk that involving the Markov chain in the problem actually makes a significant difference from the case  where there is no regime switching.

(This talk is based on a joint paper with Siyu Lv)