Characterization of stochastic equilibrium controls by the Malliavin calculus

• Main Authors: Nguwi, Jiang Yu, Privault, Nicolas
• Other Authors: School of Physical and Mathematical Sciences
• Format: Article
• Language: English
• Published: 2022
• Subjects: Science::Mathematics::Probability theory; Stochastic Maximum Principle; Spike Perturbation; Backward Stochastic Differential Equation; Malliavin Calculus
• Online Access: https://hdl.handle.net/10356/156893
• Institution: Nanyang Technological University

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.