Golden parachutes under the threat of accidents

This paper addresses a continuous-time contracting model that extends Sannikov's problem. In our model, a principal hires a risk-averse agent to carry out a project. Specifically, the agent can perform two different tasks, namely to increase the instantaneous growth rate of the project's value, and to reduce the likelihood of accidents occurring. In order to compensate for these costly actions, the principal offers a continuous stream of payments throughout the entire duration of a contract, which concludes at a random time, potentially resulting in a lump-sum payment. We examine the consequences stemming from the introduction of accidents, modeled by a compound Poisson process that negatively impact the project's value. Furthermore, we investigate whether certain economic scenarii are still characterized by a golden parachute as in Sannikov's model. A golden parachute refers to a situation where the agent stops working and subsequently receives a compensation, which may be either a lump-sum payment leading to termination of the contract or a continuous stream of payments, thereby corresponding to a pension.