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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- 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.
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Hassler, U. (2016). Introduction. In: Stochastic Processes and Calculus. Springer Texts in Business and Economics. Springer, Cham. https://doi.org/10.1007/978-3-319-23428-1_1
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DOI: https://doi.org/10.1007/978-3-319-23428-1_1
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