### Viscosity and Principal-Agnet Problem

- Series
- SIAM Student Seminar
- Time
- Friday, September 11, 2009 - 13:00 for 1 hour (actually 50 minutes)
- Location
- Skiles 255
- Speaker
- Ruoting Gong – Georgia Tech – rgong@math.gatech.edu

We develop a stochastic control system from a continuous-time
Principal-Agent model in which both the principal and the agent have
imperfect information and different beliefs about the project. We
attempt to optimize the agent’s utility function under the agent’s
belief. Via the corresponding Hamilton-Jacobi-Bellman equation we
prove that the value function is jointly continuous and satisfies the
Dynamic Programming Principle. These properties directly lead to the
conclusion that the value function is a viscosity solution of the HJB
equation. Uniqueness is then also established.