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A new stochastic Fubini-type theorem : On interchanging expectations and Itô integrals

URN to cite this document: urn:nbn:de:bvb:703-epub-4177-4

Title data

Baumann, Michael Heinrich:
A new stochastic Fubini-type theorem : On interchanging expectations and Itô integrals.
Bayreuth , 2019 . - 12 S.

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Project information

Project financing: Bundesministerium für Bildung und Forschung
Hanns-Seidel-Stiftung

Abstract

When a stochastic process is given through a stochastic integral or a stochastic differential equation (SDE), an analytical solution does not have to exist - and even if there is a closed-form solution, the derivation of this solution can be very complex. When the solution of the stochastic process is not needed but only the expected value as a function of time, the question arises whether it is possible to use the expectation operator directly on the stochastic integral or on the SDE and to somehow calculate the expectation of the process as a Riemann integral over the expectation of the integrands and integrators. In this paper, we show that if the integrator is linear in expectation, the expectation operator and an Itô integral can be interchanged. Additionally, we state how this can be used on SDEs and provide an application from the field of mathematical finance.

Further data

Item Type: Preprint, postprint
Keywords: Stochastic Analysis; Itô integral; Expectations; Fubini Theorem; Semimartingale; Stochastic Process
Subject classification: MSC (2010): 60H05, 60H10
DDC Subjects: 500 Science > 510 Mathematics
Institutions of the University: Faculties > Faculty of Mathematics, Physics und Computer Science > Department of Mathematics > Chair Applied Mathematics (Applied Mathematics)
Profile Fields > Advanced Fields > Nonlinear Dynamics
Research Institutions > Research Centres > Forschungszentrum für Modellbildung und Simulation (MODUS)
Faculties
Faculties > Faculty of Mathematics, Physics und Computer Science
Faculties > Faculty of Mathematics, Physics und Computer Science > Department of Mathematics
Profile Fields
Profile Fields > Advanced Fields
Research Institutions
Research Institutions > Research Centres
Language: English
Originates at UBT: Yes
URN: urn:nbn:de:bvb:703-epub-4177-4
Date Deposited: 13 Feb 2019 08:08
Last Modified: 14 Mar 2019 13:40
URI: https://epub.uni-bayreuth.de/id/eprint/4177

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