Introduction to stochastic finance
type: Item
instance of: scholarly article
title: Introduction to stochastic finance
zbMATH Open document ID: 1420.91001
DOI: 10.1007/978-981-13-1657-9
published in: Universitext
publication date: 2018-08-28T00:00:00Z
review text: Stochastic finance, as an important discipline, aims to investigate theoretical and applied problems, which are often motivated from practices in the finance industry, using advanced theories and techniques in probability theory and stochastic analysis. It provides an elegant and beautiful mathematical language to describe and understand randomness attributable to activities in financial markets and the economy. It throws light on deepening the understanding of randomness in financial markets. The landmark contributions by \textit{J. M. Harrison} and \textit{D. M. Kreps} [J. Econ. Theory 20, 381--408 (1979; Zbl 0431.90019)], \textit{J. M. Harrison} and \textit{S. R. Pliska} [Stochastic Processes Appl. 11, 215--260 (1981; Zbl 0482.60097); Stochastic Processes Appl. 15, 313--316 (1983; Zbl 0511.60094)] laid the foundations of stochastic finance, where the relationship between the economic notion of no-arbitrage and the martingale theory was explicitly and rigorously established. This is coined as the fundamental theorem of asset pricing which is at the heart of stochastic finance. The general theory of processes and the semimartingale calculus pioneered by the ``Strasbourg school'' led by Paul-André Meyer have been widely employed in stochastic finance. See [\textit{J. M. Harrison} and \textit{S. R. Pliska}, Stochastic Processes Appl. 11, 215--260 (1981; Zbl 0482.60097)] and this monograph by Yan (2018). It was also noted by some other authors, for example, \textit{C.F. Huang} [``Continuous-time stochastic processes'' in: The new palgrave: finance. London: Palgrave Macmillan. 110--118 (1989)] and \textit{F. Delbaen} and \textit{W. Schachermayer} [Math. Ann. 300, No. 3, 463--520 (1994; Zbl 0865.90014)], that the importance for the modern finance theory of the general theory of processes may give an impression that the general theory of processes is specially designed for the modern finance theory. Though the treatments of problems in stochastic finance may sometimes le…
reviewed by: Tak Kuen Siu
Mathematics Subject Classification ID: 91-01
Mathematics Subject Classification ID: 91G10
Mathematics Subject Classification ID: 91G20
Mathematics Subject Classification ID: 91B25
Mathematics Subject Classification ID: 91G30
Mathematics Subject Classification ID: 60G42
Mathematics Subject Classification ID: 91B16
Mathematics Subject Classification ID: 60H30
Mathematics Subject Classification ID: 62P05
Mathematics Subject Classification ID: 62M10
zbMATH DE Number: 6928408
zbMATH Keywords: stochastic finance
zbMATH Keywords: martingale theory
zbMATH Keywords: general theory of processes
zbMATH Keywords: semimartingale calculus
author: Jia-An Yan
MaRDI profile type: Publication
full work available at URL: https://doi.org/10.1007/978-981-13-1657-9
OpenAlex ID: W2897456077
description: scientific article; zbMATH DE number 6928408