Abstracts

We consider a principal-agent problem where a principal hires an agent to run a project exposed to exogenous shocks that may generate large losses. The latter can be mitigated by the agent through costly risk mitigation effort, as represented by risk monitoring systems and risk management tools. As the agent is protected by limited liability, and the principal can only observe the cashflow realizations and shock occurrences, but not the distribution of losses triggered by exogenous shocks, a moral hazard problem arises.
We show how the principal can induce the agent to exert effort, by offering contracts making provisions for the upside and the downside. We find that optimal contracts reward performance upon cumulated cashflows reaching a prescribed target. As for the downside, we find that the distribution of losses plays a fundamental role in shaping optimal incentive contracts. Under some conditions on the loss distribution, the principal commits to support the agent in his risk mitigation efforts when loss occurrences are serious, but not extreme. In other situations, the only incentive available to the principal on the downside is the threat of termination.
We then extend the baseline model by allowing the principal to provide extra resources to support the firm over time. We determine the optimal capital injection strategy and show that when injection costs are high enough the principal will support the agent only if strictly necessary in order to preserve the agent’s limited liability and keep the project alive (or preventing the firm’s liquidation/shut down).
Our contribution is related to the literature on dynamic agency in continuous-time (Holmstrom and Milgrom 1987, Biais, Mariotti, Plantin and Rochet 2007, Cadenillas, Cvitanic and Zapatero 2007, Civtanic Wan and Zhang 2006 and 2008, Civtanic, Wan and Yang 2013, Williams 2011) and uses martingale techniques developed by Sannikov (2008). The typical setting of these contributions involves Brownian risk sources (DeMarzo and Sannikov 2006), or Poisson uncertainty with predictable shock sizes (Sung 1997, Biais, Mariotti, Rochet and Villeneuve 2010). A novel feature of our model is that Poisson cashflows have unpredictable size that is affected by the agent’s actions, a setting that has interesting implications for optimal incentives in the face of downside risk. Our work is also related to techniques in stochastic control used in the literature on optimal dividends, including Paulsen and Hunt 2013, Azcue and Muler 2005, Avram et al 2007, Schmidli 2008, Albrecher and Thonhauser 2008.