时间不一致契约理论
Time-inconsistent contract theory
摘要：
本文研究了有限时间内连续支付和一次性支付的道德风险问题，涉及一个时间不一致的复杂代理人和一个标准的效用最大化委托人。基于Cvitanić、Possamação和Touzi [18]中的所谓动态规划方法以及Hernández和Possamação [43]中的最近可用结果，我们提出了一种涵盖先前收缩问题的方法。我们的主要贡献在于描述了校长所面临的道德风险问题。特别是，它表明，在相对温和的技术条件下的数据的问题，在一个较小的限制家庭的合同的委托人的期望效用的上确界等于所有可行的合同的上确界。然而，这种特性产生，据我们所知，一类新的控制问题，涉及通过Volterra型控制，和无限维随机目标约束的前向Volterra方程的控制。尽管这样一个问题的固有挑战，我们研究的解决方案下的效用函数的代理人和委托人的三种不同的规格，并得出定性的影响，从最优合同的形式。一般情况仍然是未来研究的主题。
英文摘要：
This paper investigates the moral hazard problem in finite horizon with both continuous and lump-sum payments, involving a time-inconsistent sophisticated agent and a standard utility maximiser principal. Building upon the so-called dynamic programming approach in Cvitanić, Possamaï, and Touzi [18] and the recently available results in Hernández and Possamaï [43], we present a methodology that covers the previous contracting problem. Our main contribution consists in a characterisation of the moral hazard problem faced by the principal. In particular, it shows that under relatively mild technical conditions on the data of the problem, the supremum of the principal's expected utility over a smaller restricted family of contracts is equal to the supremum over all feasible contracts. Nevertheless, this characterisation yields, as far as we know, a novel class of control problems that involve the control of a forward Volterra equation via Volterra-type controls, and infinite-dimensional stochastic target constraints. Despite the inherent challenges associated to such a problem, we study the solution under three different specifications of utility functions for both the agent and the principal, and draw qualitative implications from the form of the optimal contract. The general case remains the subject of future research.
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