Optimal contract under moral hazard with soft information

I study a model of moral hazard with soft information: the agent alone observes the stochastic outcome of her action; hence the principal faces a problem of ex post adverse selection. With limited instruments the principal cannot solve these two problems independently; the ex post incentive for misreporting interacts with the ex ante incentives for effort. The optimal transfer is option-like, the contract leaves the agent with some ex ante rent and fails to elicit truthful revelation in all states. Audit and transfer co-vary positively, which likely is a forgotten component of many real-life contracts.