A risk based approach to the principal–agent problem

Boualem Djehiche and Peter Helgesson

Asian Journal of Economics and Banking, 2024, vol. 8, issue 3, 310-334

Abstract: Purpose - We aim to generalize the continuous-time principal–agent problem to incorporate time-inconsistent utility functions, such as those of mean-variance type, which are prevalent in risk management and finance. Design/methodology/approach - We use recent advancements of the Pontryagin maximum principle for forward-backward stochastic differential equations (FBSDEs) to develop a method for characterizing optimal contracts in such models. This approach addresses the challenges posed by the non-applicability of the classical Hamilton–Jacobi–Bellman equation due to time inconsistency. Findings - We provide a framework for deriving optimal contracts in the principal–agent problem under hidden action, specifically tailored for time-inconsistent utilities. This is illustrated through a fully solved example in the linear-quadratic setting, demonstrating the practical applicability of the method. Originality/value - The work contributes to the existing literature by presenting a novel mathematical approach to a class of continuous time principal–agent problems, particularly under hidden action with time-inconsistent utilities, a scenario not previously addressed. The results offer potential insights for both theoretical development and practical applications in finance and economics.

Keywords: Principal–agent problem; Stochastic maximum principle; Pontryagin’s maximum principle; Mean-variance; Time inconsistent utility functions; B41; C00; C61; C70; C72; 93E20; 49N70; 49N90 (search for similar items in EconPapers)
Date: 2024
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Persistent link: https://EconPapers.repec.org/RePEc:eme:ajebpp:ajeb-05-2024-0065

DOI: 10.1108/AJEB-05-2024-0065

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