Elementary stochastic calculus for finance with infinitesimals

Teaching Calculus with Infinitesimals

Synopsis This article argues that first semester calculus courses for non-mathematics majors should be taught using infinitesimals. This applies to both high school and undergraduate calculus courses. The use of infinitesimals in calculus, though more intuitive than the approach developed in the 19 th century, has been controversial for over two millennia. However, in the 20 th century their us...

A Review of Stochastic Calculus for Finance

This is a review of the two-volume text Stochastic Calculus for Finance by Steven Shreve, ∗Graduate School of Business, Stanford University, Stanford CA 94305-5015. I am grateful for conversations with Julien Hugonnier and Philip Protter, for decades worth of interesting discussions with Mike Harrison, and also for the patient encouragement of the editor, Bob Devaney. Stochastic Calculus for Fi...

PDE for Finance Notes – Stochastic Calculus Review

The material presented here is covered in the books by Neftci (An Introduction to the Mathematics of Financial Derivatives), or Chang (Stochastic Optimization in Continuous Time). Deeper treatments can be found for example in Shreve (Stochastic Calculus for Finance II), Steele (Stochastic Calculus and Financial Applications), and Oksendal (Stochastic Differential Equations: an Introduction with...

Steven Shreve: Stochastic Calculus and Finance

An Introduction to Stochastic Calculus with Applications to Finance