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.

我们研究了均值-波动率联合歧义不确定性下的连续时间委托-代理问题。委托人和代理人都表现出Gilboa–Schmeidler对指数效用的极端歧义厌恶。我们区分事后实现的波动率和事前感知的波动率，并认为次优合约必然包含两个共享规则：一个是实现成果的共享规则，另一个是实现波动性的共享规则。与以往一样，成果共享规则用于不确定性共享和工作激励，波动性共享规则用于使代理人的最坏情况与委托人的最坏情况保持一致。在最佳状态下，将最坏的先验条件对称化，并且已实现的补偿与已实现的波动性呈正相关。这种理论上的正相关关系可以与流行的管理薪酬惯例（如限制性股票加股票期权授予）相一致。提供了线性二次示例的封闭形式的解决方案。