Stochastic Calculus and Differential Equations for Physics and Finance

Book Description

Stochastic provides a powerful description of a specific class of stochastic processes in physics and . However, many econophysicists struggle to understand it. This book presents the subject simply and systematically, giving graduate students and practitioners a better understanding and enabling them to apply the methods in practice. The book develops Ito calculus and Fokker-Planck equations as parallel approaches to stochastic processes, using those methods in a unified way. The focus is on nonstationary processes, and statistical ensembles are emphasized in time series . Stochastic calculus is developed using general martingales. Scaling and fat tails are presented via diffusive . Fractional Brownian motion is thoroughly analyzed and contrasted with Ito processes. The Chapman-Kolmogorov and Fokker-Planck equations are shown in and by example to be more general than a Markov process. The book also presents new ideas in economics and a critical survey of econometrics.

Table of Contents

Chapter 1 Random variables and probability distributions
Chapter 2 Martingales, Markov, and nonstationarity
Chapter 3 Stochastic calculus
Chapter 4 Ito processes and Fokker–Plan
Chapter 6 Fractional Brownian motion
Chapter 7 Kolmogorov’s pdes and Chapman–Kolmogorov
Chapter 8 Non-Markov Ito processes
Chapter 9 Black–Scholes, martingales, and Feynman–Kac
Chapter 10 Stochastic calculus with martingales
Chapter 11 Statistical physics and finance: A brief history of each
Chapter 12 Introduction to new financial economics
Chapter 13 Statistical ensembles and time-series analysis
Chapter 14 Econometrics
Chapter 15 Semimartingales

Book Details

  • Title: Stochastic Calculus and Differential Equations for Physics and Finance
  • Author:
  • Length: 215 pages
  • Edition: 1
  • Language: English
  • Publisher:
  • Publication Date: 2013-04-08
  • ISBN-10: 0521763401
  • ISBN-13: 9780521763400
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