Transcription of A Brief Introduction to Stochastic Calculus
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IEOR E4706: Foundations of Financial Engineeringc 2016 by Martin HaughA Brief Introduction to Stochastic CalculusThese notes provide a very Brief Introduction to Stochastic Calculus , the branch of mathematics that is mostidentified with financial engineering and mathematical finance. We will ignore most of the technical details andtake an engineering approach to the subject. We will only introduce the concepts that are necessary forderiving the Black-Scholes formula later in the course. These concepts include quadratic variation, stochasticintegrals and Stochastic differential equations.
2.1 Stochastic Di erential Equations De nition 9 An n-dimensional It^o process, X t, is a process that can be represented as X t = X 0 + a. = a: (7) 2 3 a 4. A Brief Introduction to Stochastic Calculus 6 1)) + ( )) + ( ) = : = + @) = ) +) + @) ...
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