AP
AMSE Publications
Book Chapter Mathematical Modeling in Physical Sciences 2022

Stochastic Differential Equations in Financial Mathematics

Amara Patel*, Sunita Krishnan * corresponding author

stochastic differential equations Black-Scholes financial mathematics Euler-Maruyama volatility models
Book ISBN: 978-1-83568-089-6 Book DOI: 10.12345/amse.mmps.2022 Published: November 2022
Authors
2
Keywords
5
Book
Mathematical Modeling in Physical S...
Series
AMA

Abstract

This paper reviews stochastic differential equations (SDEs) and their applications in financial modeling. We examine the Black-Scholes framework, Heston stochastic volatility model, and jump-diffusion processes. Numerical methods for SDE simulation including Euler-Maruyama, Milstein, and Runge-Kutta schemes are analyzed with convergence guarantees.

Keywords

stochastic differential equations Black-Scholes financial mathematics Euler-Maruyama volatility models

Authors

AP
Amara Patel Corresponding
Indian Institute of Science, Bangalore
India
amara.patel@iisc.ac.in
SK
Sunita Krishnan
IIM Bangalore
India
s.krishnan@iisb.ac.in