Hostname: page-component-8448b6f56d-jr42d Total loading time: 0 Render date: 2024-04-24T00:43:38.339Z Has data issue: false hasContentIssue false
  • English
  • Français

An alternative axiomatic characterisation of pricing operators

Part of: Miscellaneous applications of operator theory General theory of linear operators 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.
Get access Rights & Permissions [Opens in a new window]

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 

Access options

Get access to the full version of this content by using one of the access options below. (Log in options will check for institutional or personal access. Content may require purchase if you do not have access.)

References

Biagini, S. and Cont, R. (2007).Model-free representation of pricing rules as conditional expectations.In Stochastic Processes and Applications to Mathematical Finance,World Scientific,Hackensack, NJ,pp. 53–66.Google Scholar
De Jonge, E. (1979).Conditional expectation and ordering.Ann. Prob. 7,179–183.CrossRefGoogle Scholar
Delbaen, F. and Schachermayer, W. (1998).The fundamental theorem of asset pricing for unbounded stochastic processes.Math. Ann. 312,215–250.Google Scholar
Delbaen, F. and Schachermayer, W. (2006).The Mathematics of Arbitrage.Springer,Berlin.Google Scholar
Rogers, L. C. G. (1998).The origins of risk-neutral pricing and the Black‒Scholes formula.In The Handbook of Risk Management and Analysis,ed. C. Alexander,John Wiley,Chichester,pp. 81–94.Google Scholar