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

Robert Jarrow, Philip Protter

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

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.