Title data
Baumann, Michael Heinrich:
A new stochastic Fubini-type theorem : On interchanging expectations and Itô integrals.
Bayreuth
,
2019
. - 12 p.
There is a more recent version of this item available. |
Project information
Project financing: |
Bundesministerium für Bildung und Forschung Hanns-Seidel-Stiftung |
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Abstract in another language
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 |
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Keywords: | Stochastic Analysis; Itô integral; Expectations; Fubini Theorem; Semimartingale; Stochastic Process |
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 Mathematics V (Applied Mathematics) 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: | 500 Science > 510 Mathematics |
Date Deposited: | 16 Feb 2019 22:00 |
Last Modified: | 13 Apr 2021 12:36 |
URI: | https://eref.uni-bayreuth.de/id/eprint/47446 |
Available Versions of this Item
- A new stochastic Fubini-type theorem : On interchanging expectations and Itô integrals. (deposited 16 Feb 2019 22:00) [Currently Displayed]