Elementary stochastic calculus for finance with infinitesimals

Jiří Witzany

Commentationes Mathematicae Universitatis Carolinae (2017)

  • Volume: 58, Issue: 1, page 101-124
  • ISSN: 0010-2628

Abstract

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The concept of an equivalent martingale measure is of key importance for pricing of financial derivative contracts. The goal of the paper is to apply infinitesimals in the non-standard analysis set-up to provide an elementary construction of the equivalent martingale measure built on hyperfinite binomial trees with infinitesimal time steps.

How to cite

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Witzany, Jiří. "Elementary stochastic calculus for finance with infinitesimals." Commentationes Mathematicae Universitatis Carolinae 58.1 (2017): 101-124. <http://eudml.org/doc/287881>.

@article{Witzany2017,
abstract = {The concept of an equivalent martingale measure is of key importance for pricing of financial derivative contracts. The goal of the paper is to apply infinitesimals in the non-standard analysis set-up to provide an elementary construction of the equivalent martingale measure built on hyperfinite binomial trees with infinitesimal time steps.},
author = {Witzany, Jiří},
journal = {Commentationes Mathematicae Universitatis Carolinae},
keywords = {equivalent martingale measure; option pricing; stochastic processes; non-standard analysis},
language = {eng},
number = {1},
pages = {101-124},
publisher = {Charles University in Prague, Faculty of Mathematics and Physics},
title = {Elementary stochastic calculus for finance with infinitesimals},
url = {http://eudml.org/doc/287881},
volume = {58},
year = {2017},
}

TY - JOUR
AU - Witzany, Jiří
TI - Elementary stochastic calculus for finance with infinitesimals
JO - Commentationes Mathematicae Universitatis Carolinae
PY - 2017
PB - Charles University in Prague, Faculty of Mathematics and Physics
VL - 58
IS - 1
SP - 101
EP - 124
AB - The concept of an equivalent martingale measure is of key importance for pricing of financial derivative contracts. The goal of the paper is to apply infinitesimals in the non-standard analysis set-up to provide an elementary construction of the equivalent martingale measure built on hyperfinite binomial trees with infinitesimal time steps.
LA - eng
KW - equivalent martingale measure; option pricing; stochastic processes; non-standard analysis
UR - http://eudml.org/doc/287881
ER -

References

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