Abstract:

This thesis develops stochastic-control methods for dynamic principal–agent problems in continuous time. The first part studies adverse selection with moral hazard, where the agent privately observes her type. We reformulate the principal’s problem as an optimal control problem with partial information and state constraints, and characterize the value through state-constrained HJB equations. The second part studies sequential contracting with multiple lump-sum payments at fixed dates, using recursive BSDEs to reduce the Stackelberg problem to a single stochastic control problem with mixed static and continuous controls. The third part allows the principal to choose both the timing and size of discretionary bonuses, leading to a mixed control-stopping problem characterized by HJB variational inequalities. Together, the thesis shows how private information, payment timing, and contractual flexibility shape optimal incentive design.