Stochastic Calculus and an Application to the Black-scholes Model
نویسنده
چکیده
The following paper develops the basics behind stochastic calculus, which extends the theory of integration to stochastic (random) processes. The paper starts off with developing Brownian motion and its properties, which are used to develop the theory behind Itô integration. Several forms of the Itô integral are presented. A brief overview of the Radon-Nikodym and Girsanov Theorems are presented. Lastly, we present an application of stochastic calculus with the Black-Scholes Model, a model for pricing options or other claims based on the arbitrage-free price of a hedging portfolio.
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