A characterization of martingale-equivalent compound mixed Poisson process

Demetrios P. Lyberopoulos; Nikolaos D. Macheras

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arXiv · 1905.07629

A characterization of martingale-equivalent compound mixed Poisson process

Demetrios P. Lyberopoulos·Nikolaos D. Macheras

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Abstract

If a given aggregate process $S$ is a compound mixed Poisson process under a probability measure $P$, a characterization of all probability measures $Q$ on the domain of $P$, such that $P$ and $Q$ are progressively equivalent and $S$ remains a compound mixed Poisson process with improved properties, is provided. This result generalizes earlier work of Delbaen & Haezendonck (1989). 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. 2019-05-18. A characterization of martingale-equivalent compound mixed Poisson process. https://arxiv.org/abs/1905.07629

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