Optimal Monitoring Schedule in Dynamic Contracts

Consider a setting in which a principal induces effort from an agent to reduce the arrival rate of a Poisson process of adverse events. The effort is costly to the agent, and unobservable to the principal, unless the principal is monitoring the agent. Monitoring ensures effort but is costly to the principal. The optimal contract involves monetary payments and monitoring sessions that depend on past arrival times. We formulate the problem as a stochastic optimal control model and solve the problem analytically. The optimal schedules of payment and monitoring demonstrate different structures depending on model parameters, and may involve monitoring for a random period of time. Overall, the optimal dynamic contracts are simple to describe, easy to compute and implement, and intuitive to explain