用于波动率控制的强制型和对偶修正型合约
Forcing and duality-corrected contracts for volatility control
AI总结：
本文针对带漂移和波动率控制的连续时间委托代理问题，在指出现有方法最优性假设局限性的基础上，提出两类通用合约形式以修正对偶间隙，为波动率控制下的最优激励构建提供更通用方案。
AI中文摘要：
本文重新研究了带漂移和波动率控制的连续时间委托代理问题中最优激励的构建。最初，Cvitanić、Possamaï和Touzi（2018）[8]提出了一种依赖动态规划和二阶倒向随机微分方程（2BSDEs）的通用方法，用于确定该场景下的最优合约形式。最近，Chiusolo和Hubert（2026）[5]提出了一种基于倒向随机微分方程（BSDE）的方法，为主管引入了一种替代的“可合约化波动率”问题。除了提出的新方法外，本研究还强调，文献[8]的最优性结果实际上依赖于一个假设，即下文所述的假设2.3，该假设可能不普遍成立。受此启发，本文引入了一类更通用的合约，由满足一定条件的函数ψ参数化，这些条件使合约对代理人具有揭示性，且对主管而言无损失。我们进一步提供了ψ的两种自然形式：一种受BSDE方法启发，产生强制型合约；另一种受2BSDE方法启发，用于在假设2.3不成立时修正对偶间隙。
英文摘要：
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.
