Time Consistent Equilibria in Dynamic Models With Recursive Payoffs and Behavioral Discounting

Balbus, Łukasz; Reffett, Kevin; Woźny, Łukasz

doi:10.2139/ssrn.3722808

Cited by 1 publication

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References 72 publications

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“…Balbus et al. (2022) show the existence of time‐consistent equilibria for dynamic models with generalized discounting. A survey of some of the state of behavioral economics research in contract theory was provided in Kószegi (2014).…”

Section: Introductionmentioning

confidence: 99%

Time‐inconsistent contract theory

Hernández,

Possamaï

2023

Mathematical Finance

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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.

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Section: Introductionmentioning

confidence: 99%