Itovsn3: Doing Stochastic Calculus with Mathematica
This chapter describes the construction and use of Itovsn3, a Mathematica package which implements stochastic calculus (also known as Itô calculus). Stochastic calculus is of great use in mathematical finance (see for example Duffie, 1988) and therefore its implementation within computer algebra packages is likely to be of considerable interest to readers of this volume. Itovsn3 is a direct descendant of a collection of procedures (also called Itovsn3) which implement stochastic calculus in the REDUCE computer algebra language. The two implementations are similar, differing mainly in the use of the package concept (for the Mathematica version) and in the use of global substitution rules (for the REDUCE version), but both providing a simple and direct implementation based around the renowned Itô formula.
KeywordsBrownian Motion Stochastic Differential Equation Computer Algebra Stochastic Calculus Local Martingale
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