Robust Contracts in Continuous Time

We study two types of robust contracting problem under hidden action in continuous time. In type I problem, the principal is ambiguous about the project cash flows, while he is ambiguous about the agent’s beliefs in type II problem. The principal designs a robust contract that maximizes his utility under the worst-case scenario subject to the agent’s incentive and participation constraints. We implement the optimal contract by cash reserves, debt and equity. In addition to receiving ordinary dividends when cash reserves reach a threshold, outside equity holders also receive special dividends or inject cash in the cash reserves to hedge against model uncertainty. Ambiguity aversion lowers outside securities value and raises the credit yield spread. It generates equity premium for type I problem, but not for type II problem. The equity premium and the credit yield spread are state dependent and high for distressed firms with low cash reserves.