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

Title data

Baumann, Michael Heinrich:
A new stochastic Fubini-type theorem : On interchanging expectations and Itô integrals.
In: Sankhya A. (20 March 2020) . - pp. 1-13.
ISSN 0976-8378
DOI: https://doi.org/10.1007/s13171-019-00195-y

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Official URL: Volltext

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Project information

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

Abstract in another language

When a stochastic process is given through an Itô integral, i.e. 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 technical trading, i.e. from the field of mathematical finance.

Further data

Item Type: Article in a journal
Refereed: Yes
Keywords: Stochastic analysis; Itô integral; Fubini theorem; Semimartingale
Subject classification: MSC (2010): 60H05, 60H10
Institutions of the University: Faculties
Faculties > Faculty of Mathematics, Physics und Computer Science
Faculties > Faculty of Mathematics, Physics und Computer Science > Department of Mathematics
Faculties > Faculty of Mathematics, Physics und Computer Science > Department of Mathematics > Chair Applied Mathematics
Faculties > Faculty of Law, Business and Economics > Department of Economics > Chair Economics I - International Economics and Finance
Profile Fields
Profile Fields > Advanced Fields
Profile Fields > Advanced Fields > Nonlinear Dynamics
Research Institutions
Research Institutions > Research Centres
Research Institutions > Research Centres > Forschungszentrum für Modellbildung und Simulation (MODUS)
Result of work at the UBT: Yes
DDC Subjects: 300 Social sciences > 330 Economics
500 Science > 510 Mathematics
Date Deposited: 06 Apr 2020 07:10
Last Modified: 06 Apr 2020 07:10
URI: https://eref.uni-bayreuth.de/id/eprint/54844

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