Time‐inconsistent contract theory
研究了有限时间范围内存在时间不一致的成熟代理人和标准效用最大化委托人的道德风险问题，刻画了委托人的最优契约特征，并在三种效用函数设定下求解了最优契约形式。
Abstract 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 maximizer principal: Building upon the so‐called dynamic programming approach in Cvitanić et al. (2018) and the recently available results in Hernández and Possamaï (2023), we present a methodology that covers the previous contracting problem. Our main contribution consists of a characterization 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 characterization 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 with 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. We illustrate some of our results in the context of a project selection contracting problem between an investor and a time‐inconsistent manager.