A Class of Explicit optimal contracts in the face of shutdown

Understand

What type of delegation contract should be offered when facing a risk of the magnitude of the pandemic we are currently experiencing and how does the likelihood of an exogenous early termination of the relationship modify the terms of a full-commitment contract? We study these questions by considering a dynamic principal-agent model that naturally extends the classical Holmstr{\"o}m-Milgrom setting to include a risk of default whose origin is independent of the inherent agency problem.

• 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 shutdown-free Holmstr{\"o}m-Milgrom model and a linear prevention mechanism that is proportional to the random lifetime of the contract.
• We then tweak the model to add a possibility for risk mitigation through investment and study its optimality.