Jiri Witzany
580 California St., Suite 400
San Francisco, CA, 94104
Elementary stochastic calculus for finance with infinitesimals
2017, Commentationes Mathematicae Universitatis Carolinae
https://doi.org/10.14712/1213-7243.2015.192
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Abstract
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Key takeaways
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- Stochastic calculus is essential for derivatives pricing, particularly using infinitesimal time steps.
- The equivalent martingale measure theorem enables derivative valuation under adjusted probability measures.
- Infinitesimals can simplify the mathematical framework of financial models, enhancing accessibility for practitioners.
- The paper aims to make derivatives pricing techniques more approachable for financial engineers without advanced calculus training.
- Key stochastic processes, including Brownian motion, are constructed using hyperfinite binomial trees and non-standard analysis.
Figures (2)
References (30)
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