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Introduction de la spculation Preliminaries

AN Introduction TO THE stochastic INTEGRALMATT paper gives an elementary Introduction to the developmentof the stochastic integral. I aim to provide some of the foundations for some-one who wants to begin the study of stochastic calculus, which is of greatimportance in the theory of options calculus is now one of the central tools in modern Mathematical Fi-nance. Its beginnings can be traced back to L. Bachelier s 1990 dissertationThoriede la spculationin which he modeled stock prices with Brownian motion. Nearlyone hundred years later Robert Miller and Myron Scholes won the Nobel Prizeusing stochastic calculus and arbitrage pricing to derive the famed Black-Scholesequation. In this paper I will provide a hopefully gentle Introduction to stochasticcalculus via the development of the stochastic have found that in the literature there is a great divide between those introduc-tory texts which are only accessible to PhD s on the one hand, and those which lackrigor altogether and are directed towards traders.

AN INTRODUCTION TO THE STOCHASTIC INTEGRAL MATT OLSON Abstract. This paper gives an elementary introduction to the development of the stochastic integral. I aim to provide some of the foundations for some-one who wants to begin the study of stochastic calculus, which is of great

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