Random horizon principal-agent problems

Understand

We consider a general formulation of the random horizon Principal-Agent problem with a continuous payment and a lump-sum payment at termination.

• In the European version of the problem, the random horizon is chosen solely by the principal with no other possible action from the agent than exerting effort on the dynamics of the output process.
• We also consider the American version of the contract, which covers the seminal Sannikov's model, where the agent can also quit by optimally choosing the termination time of the contract.
• Our main result reduces such non-zero-sum stochastic differential games to appropriate stochastic control problems which may be solved by standard methods of stochastic control theory.