Forcing and duality-corrected contracts for volatility control

2026-07-29

AI Summary

This study addresses the challenge in continuous-time principal–agent problems where existing methods fail to construct optimal contracts under joint control of drift and volatility, due to the breakdown of key structural assumptions. To overcome this limitation, the paper introduces a general incentive contract framework parameterized by a function ψ, which simultaneously satisfies revelation and principal-losslessness properties. Within this framework, two classes of contracts are constructed: the first employs backward stochastic differential equations (BSDEs) to implement an enforcement mechanism that ensures controllability of the agent’s actions; the second leverages second-order BSDEs (2BSDEs) to correct the duality gap and recover optimality without relying on the original restrictive assumptions. This work thus transcends the dependence of prior theory on specific structural conditions and establishes a novel pathway for optimal contract design in general settings.

Abstract

In this paper, we revisit the construction of optimal incentives in continuous-time principal-agent problems with drift and volatility control. Originally, a general approach relying on dynamic programming and second-order backward stochastic differential equations (2BSDEs) was developed by Cvitanić, Possamaï, and Touzi (2018) [8] to determine the optimal form of contracts in this setting. More recently, Chiusolo and Hubert (2026) [5] proposed a BSDE-based approach by introducing an alternative `contractible-volatility' problem for the principal. In addition to the proposed new method, this work highlights that the optimality result of [8] actually hinges on an assumption, stated below as Assumption 2.3, which may not hold in general. Motivated by this, we introduce in this paper a more general class of contracts, parametrised by a function $ψ$ subject to conditions that make the contract revealing for the agent and without loss of generality for the principal. We further provide two natural specifications of $ψ$: one, inspired by the BSDE approach, yielding a forcing-type contract; the other, motivated by the 2BSDE approach, correcting the duality gap when Assumption 2.3 is not satisfied.

Problem

• principal-agent problem
• volatility control
• optimal contracts
• duality gap
• continuous-time

Innovation

• forcing contracts
• duality correction
• volatility control
• principal-agent problem
• 2BSDE