arXiv subjects

Dorian Cacitti-Holland

Publications and source records attributed to Dorian Cacitti-Holland.

2 recordsLinked to original sources

arXiv2025

Malliavin calculcus for a Hawkes process

We develop a Malliavin calculus for nonlinear Hawkes processes in the sense of Carlen and Pardoux. This approach, based on perturbations of the jump times of the process, enables the construction of a local Dirichlet form. As an application, we establish criteria for the absolute continuity of solutions to stochastic differential equations driven by Hawkes processes. We also derive sensitivity formulas for the valuation of financial derivatives with respect to model parameters.

math.PR↗

arXiv2025

Malliavin derivative and sensitivity for optimal liquidation

We prove that the solution of the backward stochastic differential equation with terminal singularity has a Malliavin derivative, which is the limit of the derivative of the approximating sequence. We also provide the asymptotic behavior of this derivative close to the terminal time. We apply this result to the regularity of the related partial differential equation and to the sensitivity of the liquidation problem.

math.PR↗