Applied Interdisciplinary Mathematics (AIM) Seminar

A dynamic contract with multiple agents is a classical decentralized decision-making problem with asymmetric information. In this talk, we will extend the single-agent dynamic incentive contract in continuous-time to a multi-agent scheme in finite horizon and allow the terminal reward to be dependent on the history of actions and incentives. Following the setup of Holmstrom and Milgrom, where they described the output process as a Brownian motion, and the subsequent work of Sannikov on the single agent model, we first derive a set of sufficient conditions for the existence of optimal contracts in the most general setting and establish the conditions under which they form a subgame perfect equilibrium. Then we show that the principal's problem can be converted to solving Hamilton-Jacobi-Bellman (HJB) equation requiring a static Nash equilibrium. Finally, we provide a framework for its solution by solving partial differential equations (PDE) derived from backward stochastic differential equations (BSDE). This talk should be of interest to the students in the AIM program as well as researchers working in Financial Mathematics/Engineering. The talk concerns joint work with Qi Luo. Speaker(s): Romesh Saigal (University of Michigan, Industrial and Operations Engineering)