道德风险下带有Knight不确定的最优动态契约设计

本文从概率统计模型本身的不确定性是本质的、不能消除掉的角度出发, 研究了Knight不确定下连续时间委托-代理问题, 其中主要考虑了代理人的道德风险对契约执行过程以及契约存续情况的影响.首先, 建立了代理人延续价值以及委托人预期利润的动态方程.其次, 运用次线性期望下的随机最优性原理, 以更加准确、深刻的方法去刻画实际委托人和代理人经济行为, 进而得到委托人效用值函数的Hamilton-Jacobi-Bellman (HJB) 方程, 并求得委托人对代理人最优支付以及代理人最优努力水平的表达式.最后, 通过理论解的数值模拟, 分析了Knight不确定对委托人和代理人最优策略以及最优契约的影响.

Dynamics of contract design with moral hazards under Knightian uncertainty

This paper studies a principal-agent problem in continuous time with ambiguity, an uncertainty except probabilistic uncertainty with the known probability distribution. The effects of an agent''s moral hazard on the execution and lasting of a contract are studied. Firstly, the dynamic equations of the agent''s continuation value as well as the principal''s expected profit are established. Then, according to the theory of stochastic optimal control and Peng''s sublinear expectation theory, the corresponding Hamilton-Jacobi-Bellman ( HJB) equation of the principal''s value function, as well as the expression of the principal''s optimal payment and the agent''s optimal effort level, is constructed. Finally, numerical simulations are provided to explain the effects of Knightian uncertainty on the optimal dynamic contract and the two parties'' optimal strategies.