Exit time risk-sensitive stochastic control problems related to systems of cooperative agents
- Dupuis, Paul
- Laschos, Vaios
- Ramanan, Kavita
2010 Mathematics Subject Classification
- Risk-sensitive stochastic control, mean-field interaction, min-max theorems
We study sequences, parametrized by the number of agents, of exit time stochastic control problems with risk-sensitive costs structures generate by unbounded costs. We identify a fully characterizing assumption, under which, each of them corresponds to a risk-neutral stochastic control problem with additive cost, and also to a risk-neutral stochastic control problem on the simplex, where the specific information about the state of each agent can be discarded. We finally prove that, under some additional assumptions, the sequence of value functions converges to the value function of a deterministic control problem.