Characterization of stochastic equilibrium controls by the Malliavin calculus

Characterization of stochastic equilibrium controls by the Malliavin calculus

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 ma...

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Bibliographic Details
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
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Institution: Nanyang Technological University
Language: English
Description
Summary: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.

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