Forcing and duality-corrected contracts for volatility control
arXiv:2607.27039
The paper studies how to design optimal contracts in continuous‑time principal‑agent models where the agent can control both drift and volatility, introducing a broader class of contracts that address a previously unnoticed assumption and providing forcing‑type and duality‑corrected specifications.
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 CvitaniÄ, 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 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 : 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.
25 pages