Simplified stochastic calculus with applications in economics and finance

Aleš Černý and Johannes Ruf

LSE Research Online Documents on Economics from London School of Economics and Political Science, LSE Library

Abstract: The paper introduces a simple way of recording and manipulating general stochastic processes without explicit reference to a probability measure. In the new calculus, operations traditionally presented in a measure-specific way are instead captured by tracing the behaviour of jumps (also when no jumps are physically present). The calculus is fail-safe in that, under minimal assumptions, all informal calculations yield mathematically well-defined stochastic processes. The calculus is also intuitive as it allows the user to pretend all jumps are of compound Poisson type. The new calculus is very effective when it comes to computing drifts and expected values that possibly involve a change of measure. Such drift calculations yield, for example, partial integro–differential equations, Hamilton–Jacobi–Bellman equations, Feynman–Kac formulae, or exponential moments needed in numerous applications. We provide several illustrations of the new technique, among them a novel result on the Margrabe option to exchange one defaultable asset for another.

Keywords: finance; drift; Emery formula; Girsanov’s theorem; simplified stochastic calculus (search for similar items in EconPapers)
JEL-codes: J1 (search for similar items in EconPapers)
Pages: 14 pages
Date: 2020-12-25
References: View references in EconPapers View complete reference list from CitEc
Citations:

Published in European Journal of Operational Research, 25, December, 2020. ISSN: 0377-2217

Downloads: (external link)
http://eprints.lse.ac.uk/108156/ Open access version. (application/pdf)

Related works:
Journal Article: Simplified stochastic calculus with applications in Economics and Finance (2021)
Working Paper: Simplified stochastic calculus with applications in Economics and Finance (2021)
This item may be available elsewhere in EconPapers: Search for items with the same title.

Export reference: BibTeX RIS (EndNote, ProCite, RefMan) HTML/Text

Persistent link: https://EconPapers.repec.org/RePEc:ehl:lserod:108156

Access Statistics for this paper

More papers in LSE Research Online Documents on Economics from London School of Economics and Political Science, LSE Library LSE Library Portugal Street London, WC2A 2HD, U.K.. Contact information at EDIRC.
Bibliographic data for series maintained by LSERO Manager ().