Giorgia Callegaro (Universität Padua)
Thursday, February 15, 2018 - 16:15
Humboldt-Universität zu Berlin, Institut für Mathematik
Rudower Chaussee 25, 12489 Berlin, Raum 1.115, 1.Etage
Forschungsseminar "Stochastische Analysis und Stochastik der Finanzmärkte"
Prof. P. Bank, Prof. D. Becherer, Prof. P. Friz, Prof. U. Horst, Prof. D. Kreher, Prof. N. Perkowski
We consider a general nonzero-sum impulse game with two players. The main mathematical contribution of the paper is a verification theorem which provides, under some regularity conditions, a suitable system of quasi-variational inequalities for the value functions and the optimal strategies of the two players. 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 Nash equilibrium and provide explicit expressions for the optimal strategies and the value functions. We also prove some asymptotic results with respect to the intervention costs. Finally, we consider two further non-symmetric examples where a Nash equilibrium is found numerically. Link to the paper: https://arxiv.org/abs/1605.00039
submitted by Sabine Bergmann (bergmann@mathematik.hu-berlin.de, 030/2093 5811)