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Published in:
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2016 | OriginalPaper | Chapter

1. Introduction

Author : Uwe Hassler

Published in: Stochastic Processes and Calculus

Publisher: Springer International Publishing

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Abstract

Stochastic calculus is used in finance and econom(etr)ics for instance for solving stochastic differential equations and handling stochastic integrals. This requires stochastic processes. Although stemming from a rather recent area of mathematics, the methods of stochastic calculus have shortly come to be widely spread not only in finance and economics. Moreover, these techniques – along with methods of time series modeling – are central in the contemporary econometric tool box. In this introductory chapter some motivating questions are brought up being answered in the course of the book, thus providing a brief survey of the topics treated.

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next chapter Basic Concepts from Probability Theory
Footnotes
1
In 1997, R.C. Merton and M.S. Scholes were awarded the Nobel prize jointly, “for a new method to determine the value of derivatives” (according to the official statement of the Nobel Committee).
 
2
R.F. Engle shared the Nobel prize “for methods of analyzing economic time series with time-varying volatility (ARCH)” (official statement of the Nobel Committee) with C.W.J. Granger.
 
3
Alternative transcriptions of his name into the Latin alphabet, Itô or Itō, are frequently used in the literature and are equally accepted. In this textbook we follow the spelling of Ito’s compatriot (Tanaka, 1996).
 
4
In 2006, Ito received the inaugural Gauss Prize for Applied Mathematics by the International Mathematical Union, which is awarded every fourth year since then.
 
5
By “log” we denote the natural logarithm to the base e.
 
6
For an introduction to calculus we recommend Trench (2013); this book is available electronically for free as a textbook approved by the American Institute of Mathematics.
 
Literature
Black, F., & Scholes, M. (1973). The pricing of options and corporate liabilities. The Journal of Political Economy, 81, 637–654.CrossRef
Dickey, D. A., & Fuller, W. A. (1979). Distribution of the estimators for autoregressive time series with a unit root. Journal of the American Statistical Association, 74, 427–431.
Engle, R. F. (1982). Autoregressive conditional heteroskedasticity with estimates of the variance of U.K. inflation. Econometrica, 50, 987–1008.
Engle, R. F., & Granger, C. W. J. (1987). Co-integration and error correction: Representation, estimation, and testing. Econometrica, 55, 251–276.CrossRef
Granger, C. W. J. (1981). Some properties of time series data and their use in econometric model specification. Journal of Econometrics, 16, 121–130.CrossRef
Merton, R. C. (1973). Theory of rational option pricing. The Bell Journal of Economics and Management Science, 4, 141–183.CrossRef
Phillips, P. C. B. (1987). Time series regression with a unit root. Econometrica, 55, 277–301.CrossRef
Tanaka, K. (1996). Time series analysis: Nonstationary and noninvertible distribution theory. New York: Wiley.
Vasicek, O. (1977). An equilibrium characterization of the term structure. Journal of Financial Economics, 5, 177–188.CrossRef
Metadata
Title
Introduction
Author
Uwe Hassler
Copyright Year
2016
Book
Stochastic Processes and Calculus

Print ISBN: 978-3-319-23427-4

Electronic ISBN: 978-3-319-23428-1

Copyright Year: 2016

DOI
https://doi.org/10.1007/978-3-319-23428-1_1

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