Читать книгу Martingales and Financial Mathematics in Discrete Time онлайн

7 страница из 24

Benoîte DE SAPORTA

Mounir ZILI

August 2021

Ever since the work of Black-Scholes-Merton [BLA 73] in 1973, the design, analysis and development of complex financial products and services have required not only an ever-greater understanding of financial theories but also a mastery of probability theory and stochastic processes.

This book introduces basic concepts of this theory, especially that of discrete-time martingales. It shows how this concept can be applied to the pricing and hedging of derivatives in financial markets. There are many texts in the existing literature that focus on financial mathematics and the evaluation of options, for example [LAM 97, SHR 04, VIN 04]. The majority of these texts consider only continuous-time models and make extensive use of Itô calculus. A few rare books such as [SHR 03] introduce discrete-time studies, but this is also done to prepare readers to understand continuous-time financial markets. The most unique feature of this book is that it is entirely devoted to discrete time and provides a detailed introduction to the construction of the rigorous mathematical tools required for the evaluation of options in financial markets. The only pre-requisite for this book is a basic understanding of probability. Several theoretical and numerical aspects are studied in this book, explored through multiple examples and exercises for which complete solutions are provided.