Jodi Dianetti
A singular stochastic control problem typically describes the situation in which an agent has to choose optimally an irreversible strategy in order to minimize a certain cost functional. In this talk we study a game of singular control, i.e. the problem of different agents where each agent faces a singular control problem parametrized by the strategies of her opponents. In a non-Markovian setting, we establish the existence of Nash equilibria. Moreover, we introduce a sequence of approximating games by forcing players to choose more regular controls, and we prove the convergence of the Nash equilibria of the approximating games to the Nash equilibria of the original game of singular control. We finally show some applications and we propose an algorithm to determine a Nash equilibrium for the game.
This talk is based on a joint work with Giorgio Ferrari.
