Journal
MATHEMATICS OF OPERATIONS RESEARCH
Volume 45, Issue 1, Pages 205-232Publisher
INFORMS
DOI: 10.1287/moor.2019.0989
Keywords
stochastic differential game; impulse control; Nash equilibrium; quasi-variational inequality
Funding
- research project New Perspectives in Stochastic Methods for Finance and Energy Markets, from the Visiting Scientist Program of the University of Padova
- Finance for Energy Market Research Centre in Paris
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We consider a general nonzero-sum impulse game with two players. The main mathematical contribution of this paper is a verification theorem that provides, under some regularity conditions, a suitable system of quasi-variational inequalities for the payoffs and the strategies of the two players at some Nash equilibrium. As an application, we study an impulse game with a one-dimensional state variable, following a real-valued scaled Brownian motion, and two players with linear and symmetric running payoffs. We fully characterize a family of Nash equilibria and provide explicit expressions for the corresponding equilibrium strategies and payoffs. We also prove some asymptotic results with respect to the intervention costs. Finally, we consider two further nonsymmetric examples where a Nash equilibrium is found numerically.
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