Stochastic costly state verification and dynamic contracts

I consider a dynamic costly state verification environment in which a risk-averse agent enters into a contract with a risk-neutral principal. The agent has random income which is unknown to the principal but can be verified at a cost. The principal can commit to executing random verifications.I extend the standard recursive methods to study the problem and show that it is optimal to set verification probabilities strictly less than 1. If the agent's absolute risk aversion declines sufficiently slowly, the principal will use verification regardless of its cost. If the agent's income is verified then he would get consumption and continuation utility strictly higher than if his income were not verified.