Discrete-Time Approximations and Limit Theorems: In Applications to Financial Markets

Yuliya Mishura; Kostiantyn Ralchenko

Published by De Gruyter 2021

Discrete-Time Approximations and Limit Theorems

In Applications to Financial Markets

Yuliya Mishura and Kostiantyn Ralchenko

Volume 2 in the series De Gruyter Series in Probability and Stochastics

https://doi.org/10.1515/9783110654240

Overview
Contents

About this book

Financial market modeling is a prime example of a real-life application of probability theory and stochastics. This authoritative book discusses the discrete-time approximation and other qualitative properties of models of financial markets, like the Black-Scholes model and its generalizations, offering in this way rigorous insights on one of the most interesting applications of mathematics nowadays.

An authoritative book on financial market modeling
Studies the discrete approximation, the parameter dependence and the asymptotics of financial models
Of interest to researchers and graduate students in mathematics as well in financial applications

Author / Editor information

Yuliya Mishura and Kostiantyn Ralchenko, Taras Shevchenko National University of Kyiv, Ukraine.

Reviews

"This book is an in-depth study of the relationship between discrete-time (‘real’) market models and their continuous-time counterparts, which are widely used in quantitative finance analysis due to their mathematical simplicity. […] In conclusion, "Discrete-Time Approximations and Limit Theorems" is a standout contribution to the study of option pricing and hedging problems for both discrete-time and continuous-time models. The book's thoroughness and rigor make it an indispensable reference for researchers and practitioners in the field of quantitative finance."

Prof. Dr. Elisa Alòs, Barcelona School of Economics, Spain, July 2023

Topics

Frontmatter Publicly Available Download PDF	I
Introduction Publicly Available Download PDF	V
Contents Publicly Available Download PDF	IX
Abbreviations and notations Publicly Available Download PDF	XV
1 Financial markets. From discrete to continuous time Requires Authentication Unlicensed Licensed Download PDF	1
2 Rate of convergence of asset and option prices 2.1 The rate of convergence of option prices when the limit is a Black–Scholes model Requires Authentication Unlicensed Licensed Download PDF	109
3 Limit theorems for markets with non-random time-varying coefficients Requires Authentication Unlicensed Licensed Download PDF	243
4 Convergence of stochastic integrals in application to financial markets Requires Authentication Unlicensed Licensed Download PDF	279
A Essentials of calculus, probability, and stochastic processes Requires Authentication Unlicensed Licensed Download PDF	319
Bibliography Requires Authentication Unlicensed Licensed Download PDF	363
Index Requires Authentication Unlicensed Licensed Download PDF	371

(Deutsch)

Language: English
Publisher: De Gruyter
Audience: Researchers and graduate students in probability theory, stochastics and financial mathematics.
Pages
- Front matter: 16
- Main content: 374
Illustrations
- Illustrations: 3
- Coloured Illustrations: 1
Keywords: Black-Scholes-Modell; Grenzwertsatz; Kreditmarkt

eBook

Published: October 25, 2021
ISBN: 9783110654240

Hardcover

Published: November 8, 2021
ISBN: 9783110652796