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April 2021 A characterization of martingale-equivalent mixed compound Poisson processes
Demetrios P. Lyberopoulos, Nikolaos D. Macheras
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Ann. Appl. Probab. 31(2): 778-805 (April 2021). DOI: 10.1214/20-AAP1604

Abstract

If a given aggregate process S is a mixed compound Poisson process under a probability measure P, we provide a characterization of all probability measures Q on the domain of P, such that P and Q are progressively equivalent and S remains a mixed compound Poisson process with improved properties. This result generalizes earlier work of Delbaen and Haezendonck (Insurance Math. Econom. 8 (1989) 269–277). Implications related to the computation of premium calculation principles in an insurance market possessing the property of no free lunch with vanishing risk are also discussed.

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Demetrios P. Lyberopoulos. Nikolaos D. Macheras. "A characterization of martingale-equivalent mixed compound Poisson processes." Ann. Appl. Probab. 31 (2) 778 - 805, April 2021. https://doi.org/10.1214/20-AAP1604

Information

Received: 1 September 2019; Revised: 1 May 2020; Published: April 2021
First available in Project Euclid: 1 April 2021

Digital Object Identifier: 10.1214/20-AAP1604

Subjects:
Primary: 91B30
Secondary: 28A50 , 60G44 , 60G51 , 60G55

Keywords: martingale , martingale-equivalent measures , Mixed compound Poisson process , premium calculation principle , regular conditional probability

Rights: Copyright © 2021 Institute of Mathematical Statistics

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Vol.31 • No. 2 • April 2021
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