JSTOR Daily

On the approximations of solutions to stochastic differential delay equations with Poisson random measure via Taylor series

Abstract.The subject of this paper is the analytic approximation of solution to stochastic differential delay equations with Poisson jump. We introduce approximate methods for stochastic differential ...
JSTOR Daily

Existence and Approximation of Solutions to an Infinite Set of Linear Time-Invariant Differential Equations

Sufficient conditions are given for the existence, uniqueness and finite-dimensional approximation of the solution to a first-order infinite-dimensional vector differential equation. Given a suitable ...
Nature

Stochastic Differential Equations and Asymptotic Analysis in Finance

Stochastic differential equations (SDEs) are at the heart of modern financial modelling, providing a framework that accommodates the inherent randomness observed in financial markets. These equations ...
uni

Prof. Dr. Arnulf Jentzen, Angewandte Mathematik Münster: Institut für Analysis und Numerik

Field of expertise: Numerical analysis, machine learning and scientific computing Selected Projects • Mathematical Theory for Deep Learning It is the key goal of this project to provide a rigorous ...
Risk

A mixed Monte Carlo and partial differential equation variance reduction method for foreign exchange options under the Heston–Cox–Ingersoll–Ross model

In this paper, we consider the valuation of European and path-dependent options in foreign exchange markets when the currency exchange rate evolves according to the Heston model combined with the ...