Institute of Mathematical Statistics Lecture Notes - Monograph Series

A short history of stochastic integration and mathematical finance: the early years, 1880–1970

Robert Jarrow and Philip Protter

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Abstract

We present a history of the development of the theory of Stochastic Integration, starting from its roots with Brownian motion, up to the introduction of semimartingales and the independence of the theory from an underlying Markov process framework. We show how the development has influenced and in turn been influenced by the development of Mathematical Finance Theory. The calendar period is from 1880 to 1970.

Chapter information

Source
Anirban DasGupta, ed., A Festschrift for Herman Rubin (Beachwood, Ohio, USA: Institute of Mathematical Statistics, 2004), 75-91

Dates
First available in Project Euclid: 28 November 2007

Permanent link to this document
https://projecteuclid.org/euclid.lnms/1196285381

Digital Object Identifier
doi:10.1214/lnms/1196285381

Mathematical Reviews number (MathSciNet)
MR2126888

Zentralblatt MATH identifier
1268.01017

Subjects
Primary: 01A60: 20th century 60H05: Stochastic integrals 60H30: Applications of stochastic analysis (to PDE, etc.) 60G44: Martingales with continuous parameter 60G35: Signal detection and filtering [See also 62M20, 93E10, 93E11, 94Axx] 60G46: Martingales and classical analysis 91B70: Stochastic models 91B28 91B99: None of the above, but in this section 60J45: Probabilistic potential theory [See also 31Cxx, 31D05] 60J55: Local time and additive functionals 60J65: Brownian motion [See also 58J65]

Keywords
stochastic integration semimartingales martingales Brownian motion Markov processes Black-Scholes options warrants contingent claims hedging strategies Bachelier homogeneous chaos history of mathematics

Rights
Copyright © 2004, Institute of Mathematical Statistics

Citation

Jarrow, Robert; Protter, Philip. A short history of stochastic integration and mathematical finance: the early years, 1880–1970. A Festschrift for Herman Rubin, 75--91, Institute of Mathematical Statistics, Beachwood, Ohio, USA, 2004. doi:10.1214/lnms/1196285381. https://projecteuclid.org/euclid.lnms/1196285381


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