We derive a characterization of equilibrium controls in continuous-time, time-inconsistent control (TIC) problems using the Malliavin calculus. For this, the classical duality analysis of adjoint BSDEs is replaced with the Malliavin integration by parts. This results into a necessary and sufficient maximum principle which is applied to a linear-quadratic TIC problem, recovering previous results obtained by duality analysis in the mean-variance case, and extending them to the linear-quadratic setting. We also show that our results apply beyond the linear-quadratic case by treating the generalized Merton problem.

中文翻译：

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Malliavin 演算对随机平衡控制的表征

我们使用 Malliavin 演算得出了连续时间、时间不一致控制 (TIC) 问题中平衡控制的特征。为此，伴随 BSDE 的经典对偶分析被 Malliavin 部分积分取代。这导致了一个必要且充分的最大原理，该原理应用于线性二次 TIC 问题，恢复了在均值方差情况下通过对偶分析获得的先前结果，并将它们扩展到线性二次设置。我们还表明，通过处理广义 Merton 问题，我们的结果适用于线性二次案例之外。