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Two results on dynamic extensions of deviation measures

Part of: Stochastic analysis Mathematical economics

Published online by Cambridge University Press:  16 July 2020

Mitja Stadje
Mitja Stadje*
Affiliation:
Ulm University
*
*Postal address: Institute of Insurance Science and Institute of Financial Mathematics, Faculty of Mathematics and Economics, Ulm University, Helmholtzstrasse 20, 89081 Ulm, Germany. Email address: mitja.stadje@uni-ulm.de
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Abstract

We give a dynamic extension result of the (static) notion of a deviation measure. We also study distribution-invariant deviation measures and show that the only dynamic deviation measure which is law invariant and recursive is the variance.

Keywords

Deviation measuretime consistencylaw invariance

MSC classification

Primary: 60H30: Applications of stochastic analysis (to PDE, etc.)
Secondary: 91B30: Risk theory, insurance 91B06: Decision theory 91B70: Stochastic models
Type
Research Papers
Information
Journal of Applied Probability , Volume 57 , Issue 2 , June 2020 , pp. 531 - 540
Copyright
© Applied Probability Trust 2020

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