Xiaolu Tan (The Chinese University of Hong Kong) Titre: Bank-El Karoui's representation of stochastic processes and its applications in the exit contract problems Abstract: We first recall Bank-El Karoui's representation theorem for stochastic processes and then provide a mean-field extension of the theorem. Next, we study an exit contract optimization problem, where the principal provides a universal exit contract to (finitely or infinitely) many heterogeneous agents. Under the universal exit contract, the agents may have different optimal exit times. The problem consists in finding the optimal contract from the principal's point of view. Under a technical monotone condition, the exit contract problem can be solved by the representation theorems. Finally, we provide some more concrete applications of the theory in the compensation problems of the electricity/energy market. Download slides