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Simplified stochastics calculus with applications in Economics and Finance

Černý, A. ORCID: 0000-0001-5583-6516 and Ruf, J. (2020). Simplified stochastics calculus with applications in Economics and Finance. European Journal of Operational Research, doi: 10.1016/j.ejor.2020.12.037

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.

Publication Type: Article
Additional Information: © 2021. This manuscript version is made available under the CC-BY-NC-ND 4.0 license http://creativecommons.org/licenses/by-nc-nd/4.0/
Publisher Keywords: finance; drift; Emery formula; Girsanov’s theorem; simplified stochastic calculus
Subjects: H Social Sciences > HB Economic Theory
H Social Sciences > HG Finance
Departments: Business School > Finance
Date Deposited: 04 Jan 2021 15:29
URI: https://openaccess.city.ac.uk/id/eprint/25430
[img] Text - Accepted Version
This document is not freely accessible until 25 December 2022 due to copyright restrictions.
Available under License Creative Commons Attribution Non-commercial No Derivatives.

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