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2009 A note on stochastic integration with respect to optional semimartingales
Christoph Kühn, Maximilian Stroh
Author Affiliations +
Electron. Commun. Probab. 14: 192-201 (2009). DOI: 10.1214/ECP.v14-1465


In this note we discuss the extension of the elementary stochastic Ito-integral w.r.t. an optional semimartingale. The paths of an optional semimartingale possess limits from the left and from the right, but may have double jumps. This leads to quite interesting phenomena in integration theory. <br> We find a mathematically tractable domain of general integrands. The simple integrands are embedded into this domain. Then, we characterize the integral as the unique continuous and linear extension of the elementary integral and show completeness of the space of integrals. Thus our integral possesses desirable properties to model dynamic trading gains in mathematical finance when security price processes follow optional semimartingales.


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Christoph Kühn. Maximilian Stroh. "A note on stochastic integration with respect to optional semimartingales." Electron. Commun. Probab. 14 192 - 201, 2009.


Accepted: 12 May 2009; Published: 2009
First available in Project Euclid: 6 June 2016

zbMATH: 1191.60068
MathSciNet: MR2505175
Digital Object Identifier: 10.1214/ECP.v14-1465

Primary: 60G48
Secondary: 60H05 , 91B28

Keywords: dynamic portfolio choice , optional semimartingales , stochastic integration theory

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