Elementary stochastic calculus for finance with infinitesimals

DOI10.14712/1213-7243.2015.192zbMath1424.60070OpenAlexW2651120361MaRDI QIDQ5270024

Jiri Witzany

Publication date: 28 June 2017

Published in: Commentationes Mathematicae Universitatis Carolinae (Search for Journal in Brave)

Full work available at URL: https://doi.org/10.14712/1213-7243.2015.192

zbMATH Keywords

stochastic processesequivalent martingale measureoption pricingnon-standard analysis

Mathematics Subject Classification ID

Applications of stochastic analysis (to PDEs, etc.) (60H30) Derivative securities (option pricing, hedging, etc.) (91G20) Stochastic integrals (60H05)

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Cites Work

• Stochastic calculus with infinitesimals
• Nonlinear stochastic integrals for hyperfinite Lévy processes
• Loeb measures in practice: Recent advances. EMS lectures 1997
• Stochastic calculus for finance. I: The binomial asset pricing model.
• Stochastic calculus for finance. II: Continuous-time models.
• An infinitesimal approach to stochastic analysis
• Elementary Extensions of Models of the Alternative Set Theory
• Radically Elementary Probability Theory. (AM-117)
• Conversion from Nonstandard to Standard Measure Spaces and Applications in Probability Theory
• A nonstandard representation for Brownian motion and Itô integration
• Internal set theory: A new approach to nonstandard analysis
• A nonstandard treatment of options driven by poisson processes
• A Nonstandard Approach to Option Pricing
• From discrete to continuous stochastic calculus
• Option pricing: A simplified approach
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