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A characterization of equivalent martingale measures in a renewal risk model with applications to premium calculation principles
Volume 7, Issue 1 (2020), pp. 43–60
Nikolaos D. Macheras   Spyridon M. Tzaninis  

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https://doi.org/10.15559/20-VMSTA148
Pub. online: 20 February 2020      Type: Research Article      Open accessOpen Access

Received
19 April 2019
Revised
3 February 2020
Accepted
3 February 2020
Published
20 February 2020

Abstract

Generalizing earlier work of Delbaen and Haezendonck for given compound renewal process S under a probability measure P we characterize all probability measures Q on the domain of P such that Q and P are progressively equivalent and S remains a compound renewal process under Q. As a consequence, we prove that any compound renewal process can be converted into a compound Poisson process through a change of measures and we show how this approach is related to premium calculation principles.

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Keywords
Compound renewal process change of measures martingale martingale measures progressively equivalent (martingale) measures premium calculation principle

MSC2010
60G55 91B30 28A35 60A10 60G44 60K05

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