标题： 时间不一致契约理论 显示英文标题

标题： Time-inconsistent contract theory

摘要： 本文研究了在有限时间范围内同时涉及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精明代理人和一个标准效用最大化委托人。 在Cvitanić、Possamaï和Touzi [18]所谓的动态规划方法以及Hernández和Possamaï [43]最近获得的结果基础上，我们提出了一种涵盖先前契约问题的方法。 我们的主要贡献在于对委托人所面临的道德风险问题的特征描述。 具体来说，它表明在问题数据上相对温和的技术条件下，委托人在一个较小的契约受限族上的期望效用上确界等于所有可行契约上的上确界。 然而，据我们所知，这种特征描述产生了一类新颖的控制问题，这些问题涉及通过伏特拉型控制来控制前向伏特拉方程，以及无限维随机目标约束。 尽管存在此类问题的固有挑战，我们研究了在代理人和委托人效用函数三种不同规范下的解，并从最优契约的形式中得出了定性结论。 一般情况仍然是未来研究的主题。 显示英文摘要

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 Cvitani\'c, Possama\"i, and Touzi [18] and the recently available results in Hern\'andez and Possama\"i [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.