Knight不确定下单边有限承诺连续时间契约问题

Continuous-time contracting problems with one-sided limited commitment under Knightian uncertainty

研究了在Knight不确定下单边有限承诺的最优契约设计问题.首先,基于Knight不确定代理人的禀赋和委托人返还给代理人的消费,在代理人消费预期效用(代理人延续价值)不低于代理人外部期权价值(保持代理人参与约束)下,设计委托人预期收益最大化的代理人单边有限承诺最优契约.利用非线性期望下的动态规划原理得到委托人最大预期效用值函数所满足的HJB方程.其次,在非线性期望下,建立了委托人价值函数的弱和强对偶定理,并获得了最优契约的判定定理.最后,针对一个消费问题的例子,对所得最优策略进行了数值模拟和经济学分析.

The optimal contract design problem with one-sided limited commitment under Knightian uncertainty was studied.First,based on the agent’s endowment process and the consumption returned by the principal under Knightian uncertainty,the contract model was established with the agent’s one-side limited commitment which characterizes the maximization of the principal expected profit under the agent’s expected utility(the agent’s continuation value)being not lower than the agent’s outside option value(keeping the participation constraint).By using the dynamic programming principle under Peng’s sublinear expectation theory,the Hamilton-Jacobi-Bellman(HJB)equation of the principal’s value function on her maximal expected utility was derived.Next,using the sublinear theory,the weak and strong dual theorems and the verification theorem of optimal strategy were obtained.Finally,for an example of consumption,the numerical simulation for results and the corresponding economic analysis were provided.