Samaneh Sojudi | Searcharxiv

arXiv2026

Conditional Expectation expression in mean-field SDEs and its applications

This study developed a novel formulation of conditional expectations within the framework of a jump-diffusion mean-field stochastic differential equation. We introduce an integrated approach that combines unconditioned expectations with rigorously defined weighting factors, employing Malliavin calculus on Poisson space and directional derivatives to enhance estimation accuracy. \noindent The proposed method is applied to the numerical pricing of American put options in a jump-diffusion mean-field setting, addressing the challenges proposed by early-exercise features. Comprehensive numerical experiments demonstrate substantial improvements in pricing accuracy compared with conventional techniques.

math.PR↗

arXiv2025

Sensitivity Analysis for Mean-Field SDEs With Jump By Malliavin Calculus: Chaos Expansion Approach

In this paper, we describe an explicit extension formula in sensitivity analysis regarding the Malliavin weight for jump-diffusion mean-field stochastic differential equations whose local Lipschitz drift coefficients are influenced by the product of the solution and its law. We state that these extended equations have unique Malliavin differentiable solutions in Wiener-Poisson space and establish the sensitivity analysis of path-dependent discontinuous payoff functions. It will be realized after finding a relation between the stochastic flow of the solutions and their derivatives. The Malliavin derivatives are defined in a chaos approach in which the chain rule is not held. The convergence of the Euler method to approximate Delta Greek is proved. The simulation experiment illustrates our results to compute the Delta, in the context of financial mathematics, and demonstrates that the Malliavin Monte-Carlo computations applied in our formula are more efficient than using the finite difference method directly.

math.PR↗