Department of Industrial Engineering & Decision Analysis [IEDA/MATH Joint Seminar] - A Representation of Stochastic Processes and its Applications in the Exit Contract Problem

We recall a classical representation theorem of stochastic processes due to Bank and El Karoui, and then introduce a mean-field extension. This representation theorem is closely related to the optimal stopping theory. We next provide some applications in the exit contract theory, where there is one principal and (finitely or infinitely) many agents. The principal provides a universal exit contract to all agents, and the agents may be heterogenous so that they would react with different stopping times. The principal's problem consists in finding an optimal universal exit contract. By use of the representation theorem, we decouple the principal's initial problem and reformulate it into an equivalent control problem.