Optimal contracting under mean-volatility joint ambiguity uncertainties

Abstract

We examine a continuous-time principal-agent problem under mean-volatility joint ambiguity uncertainties. Both the principal and the agent exhibit Gilboa–Schmeidler’s extreme ambiguity aversion with exponential utilities. We distinguish between expost realized and exante perceived volatilities, and argue that the second-best contract necessarily consists of two sharing rules: one for realized outcome and the other for realized volatility. The outcome-sharing rule is for uncertainty sharing and work incentives, as usual, and the volatility-sharing rule is to align the agent’s worst prior with that of the principal. At optimum, their worst priors are symmetrized, and realized compensation is positively related to realized volatility. This theoretical positive relation can be consistent with popular managerial compensation practices such as restricted stock plus stock option grants. A closed-form solution to a linear-quadratic example is provided.