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An alternative axiomatic characterisation of pricing operators

Part of: General theory of linear operators Miscellaneous applications of operator theory Stochastic processes Mathematical economics

Published online by Cambridge University Press:  09 December 2016

Stefan Kassberger  and
Thomas Liebmann
Stefan Kassberger*
Affiliation:
Frankfurt School of Finance and Management
Thomas Liebmann*
Affiliation:
Frankfurt School of Finance and Management
*
* Postal address: Frankfurt School of Finance and Management, Sonnemannstr. 9‒11, 60314 Frankfurt am Main, Germany.
* Postal address: Frankfurt School of Finance and Management, Sonnemannstr. 9‒11, 60314 Frankfurt am Main, Germany.
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Abstract

In the spirit of the axiomatic approach by Rogers (1998) we show the equivalence between a set of assumptions on the behaviour of prices and the existence of a representation of these prices as conditional expectations. We rely on only weak assumptions and avoid any a priori modelling of negligible events or of any market filtration. Rather, both endogenously emerge along with the representation as conditional expectations.

Keywords

Axiomatic characterisationconditional expectationmartingalepricing operator

MSC classification

Primary: 91B70: Stochastic models
Secondary: 60G44: Martingales with continuous parameter 47A67: Representation theory 47N20: Applications to differential and integral equations
Type
Short Communications
Information
Journal of Applied Probability , Volume 53 , Issue 4 , December 2016 , pp. 1257 - 1264
Copyright
Copyright © Applied Probability Trust 2016 

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References

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