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Volume 8 - Isuue 3 | November

A risk based approach to the principal–agent problem

Boualem Djehiche, and Peter Helgesson

05/12/2024 14 0 0
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Principal–agent problem Stochastic maximum principle Pontryagin’s maximum principle Mean-variance Time inconsistent utility functions.

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.

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JEL classification: B41,C00,C61,C70,C72

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