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

We use a white noise approach to Malliavin calculus to prove the following white noise generalization of the Clark-Haussmann-Ocone formula F (ω) = E[F ] + T 0 E[D t F |F t ] W (t)dt Here E[F ] denotes the generalized expectation, D t F (ω) = dF dω is the (generalized) Malliavin derivative, is the Wick product and W (t) is 1-dimensional Gaussian white noise. The formula holds for all f ∈ G * ⊃ L...

A stochastic calculus similar to Malliavin’s calculus is worked out for Brownian excursions. The analogue of the Malliavin derivative in this calculus is not a differential operator, but its adjoint is (like the Skorohod integral) an extension of the Itô integral. As an application, we obtain an expression for the integrand in the stochastic integral representation of square integrable Wiener f...

This study investigates the influence of risk tolerance on expected utility in long run. We estimate extent to which optimal portfolios is affected by small changes tolerance. For this purpose, we adopt Malliavin calculus method and Hansen–Scheinkman decomposition, through expressed terms eigenvalues eigenfunctions an operator. conclude that aversion determined these

This work concerns continuous-time, continuous-space stochastic dynamical systems described by differential equations (SDE). It presents a new approach to compute probabilistic safety regions, namely sets of initial conditions the SDE associated trajectories that are safe with probability larger than given threshold. The introduces functional is minimised at border region, then solves an optimi...

Abstract We study the optimal portfolio problem for an insider, in the case that the performance is measured in terms of the logarithm of the terminal wealth minus a term measuring the roughness and the growth of the portfolio. We give explicit solutions in some cases. Our method uses Malliavin calculus and stochastic calculus of forward integrals. We obtain new results about the enlargement of...