In this paper we study numerical methods to approximate the adapted solutions to a class of forward-backward stochastic differential equations (FBSDE's). The almost sure uniform convergence as well as ...

Exponential integrators represent an innovative class of numerical methods designed to address the challenges posed by stiff differential equations. By incorporating the matrix exponential to treat ...

We propose a new approach to constructing weak numerical methods for finding solutions to stochastic systems with small noise. For these methods we prove an error ...

Covers finite difference, finite element, finite volume, pseudo-spectral, and spectral methods for elliptic, parabolic, and hyperbolic partial differential equations. Prereq., APPM 5600. Recommended ...

Introductory course on using a range of finite-difference methods to solve initial-value and initial-boundary-value problems involving partial differential equations. The course covers theoretical ...

Analysis and implementation of numerical methods for random processes: random number generators, Monte Carlo methods, Markov chains, stochastic differential equations, and applications. Recommended ...

Studies properties and solutions of partial differential equations. Covers methods of characteristics, well-posedness, wave, heat and Laplace equations, Green's functions, and related integral ...

This paper offers a Bayesian framework for the calibration of financial models using neural stochastic differential equations ...

In this paper, a partial differential equation model for the pricing of pension plans based on average salary is posed by using the dynamic hedging methodology. The existence and uniqueness of ...