Stochastic Analysis for Finance with Simulations

  • Geon Ho Choe

Part of the Universitext book series (UTX)

Table of contents

  1. Front Matter
    Pages i-xxxii
  2. Introduction to Financial Mathematics

    1. Front Matter
      Pages 1-1
    2. Geon Ho Choe
      Pages 3-14
    3. Geon Ho Choe
      Pages 15-22
  3. Probability Theory

    1. Front Matter
      Pages 23-23
    2. Geon Ho Choe
      Pages 25-40
    3. Geon Ho Choe
      Pages 41-74
    4. Geon Ho Choe
      Pages 75-89
    5. Geon Ho Choe
      Pages 91-107
  4. Brownian Motion

    1. Front Matter
      Pages 109-109
    2. Geon Ho Choe
      Pages 111-135
    3. Geon Ho Choe
      Pages 137-145
    4. Geon Ho Choe
      Pages 147-156
  5. Itô Calculus

    1. Front Matter
      Pages 157-157
    2. Geon Ho Choe
      Pages 159-175
    3. Geon Ho Choe
      Pages 177-202
    4. Geon Ho Choe
      Pages 203-223
    5. Geon Ho Choe
      Pages 225-235
  6. Option Pricing Methods

    1. Front Matter
      Pages 237-237
    2. Geon Ho Choe
      Pages 239-253

About this book


This book is an introduction to stochastic analysis and quantitative finance; it includes both theoretical and computational methods. Topics covered are stochastic calculus, option pricing, optimal portfolio investment, and interest rate models. Also included are simulations of stochastic phenomena, numerical solutions of the Black–Scholes–Merton equation, Monte Carlo methods, and time series. Basic measure theory is used as a tool to describe probabilistic phenomena.  

The level of familiarity with computer programming is kept to a minimum. To make the book accessible to a wider audience, some background mathematical facts are included in the first part of the book and also in the appendices. This work attempts to bridge the gap between mathematics and finance by using diagrams, graphs and simulations in addition to rigorous theoretical exposition. Simulations are not only used as the computational method in quantitative finance, but they can also facilitate an intuitive and deeper understanding of theoretical concepts.  

Stochastic Analysis for Finance with Simulations is designed for readers who want to have a deeper understanding of the delicate theory of quantitative finance by doing computer simulations in addition to theoretical study. It will particularly appeal to advanced undergraduate and graduate students in mathematics and business, but not excluding practitioners in finance industry.  


Brownian Motion Stochastic Calculus Stochastic Differential Equation Option Pricing Binomial Tree Method Black–Scholes–Merton Equation Martingale Method Optimal Portfolio Interest Rate Model Monte Carlo Method Time Series

Authors and affiliations

  • Geon Ho Choe
    • 1
  1. 1.Department of Mathematical Sciences and Graduate School of FinanceKorea Advanced Institute of Science and TechnologyDaejeonKorea (Republic of)

Bibliographic information

  • DOI
  • Copyright Information Springer International Publishing Switzerland 2016
  • Publisher Name Springer, Cham
  • eBook Packages Mathematics and Statistics
  • Print ISBN 978-3-319-25587-3
  • Online ISBN 978-3-319-25589-7
  • Series Print ISSN 0172-5939
  • Series Online ISSN 2191-6675
  • About this book
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