A New Approach to Principal-Agent Problems with Volatility Control

Explore a mathematical conference talk presenting an innovative approach to solving continuous-time principal-agent problems with volatility control. Learn about an alternative formulation that simplifies the resolution process by using standard backward stochastic differential equations (BSDEs) instead of the more complex second-order BSDEs traditionally required. Discover how this new methodology leverages the principal's ability to observe and compute the quadratic variation of output processes pathwise, leading to a reformulation where the principal directly controls this process in a 'first-best' setting. Understand how Sannikov's trick is applied to resolve this alternative problem and how the solution coincides with the original problem's solution while avoiding the complexity of second-order BSDEs. Examine the practical implications of this approach, which offers greater accessibility for solving continuous-time principal-agent problems across various fields. Delve into extensions of this methodology to more complex multi-agent frameworks and gain insights into current research developments in mathematical finance and probability theory. This presentation was delivered at the Centre International de Rencontres Mathématiques during a thematic meeting honoring René Carmona, providing cutting-edge research perspectives on principal-agent theory and stochastic control.