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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. [ABSTRACT FROM AUTHOR]

We construct differential forms of all orders and a covariant derivative together with its adjoint on the probability space of a standard Poisson process, using derivation operators. In this framewok we derive a de Rham-Hodge-Kodaira decomposition as well as Weitzenböck and Clark-Ocone formulas for random differential forms. As in the Wiener space setting, this construction provides two distinct approaches to the vanishing of harmonic differential forms. [ABSTRACT FROM AUTHOR]

In this paper, we derive a formula for the expectation of random Hermite polynomials in Skorohod integrals, extending classical results in the adapted case. As an application we recover, under simple conditions and with short proofs, the anticipative Girsanov identity and quasi-invariance results obtained in Ref. 6 for quasi-nilpotent shifts on the Wiener space. [ABSTRACT FROM AUTHOR]