Stochastic differential equations (SDEs) provide a powerful framework for modelling systems where randomness plays a crucial role. Estimation methods for SDEs seek to infer underlying parameters that ...

Backward stochastic differential equations (BSDEs) have emerged as a pivotal mathematical tool in the analysis of complex systems across finance, physics and engineering. Their formulation, generally ...

SIAM Journal on Numerical Analysis, Vol. 49, No. 5/6 (2011), pp. 2017-2038 (22 pages) General autonomous stochastic differential equations (SDEs) driven by one-dimensional Brownian motion in the ...

This paper presents a novel and direct approach to solving boundary- and final-value problems, corresponding to barrier options, using forward pathwise deep learning and forward–backward stochastic ...

(Conditional) generative adversarial networks (GANs) have had great success in recent years, due to their ability to approximate (conditional) distributions over extremely high-dimensional spaces.

The whole picture of Mathematical Modeling is systematically and thoroughly explained in this text for undergraduate and graduate students of mathematics, engineering, economics, finance, biology, ...