Risk-sharing and optimal contracts with large exogenous risks

We consider a dynamic principal-agent model that naturally extends the classical Holmstrom-Milgrom setting to include a risk capable of stopping production completely. We obtain an explicit characterization of the optimal wage along with the optimal action provided by the agent. The optimal contract is linear by offering both a fixed share of the output which is similar to the standard Holmstrom-Milgrom model and a linear prevention mechanism that is proportional to the random lifetime of the contract. We then extend the model by allowing insurable risks where the agent can control the intensity of the failure by exerting an additional costly effort.