A characterization of martingale-equivalent compound mixed Poisson process

Demetrios P. Lyberopoulos; Nikolaos D. Macheras

A characterization of martingale-equivalent compound mixed Poisson process

Probability 2019-05-21 v1

Authors: Demetrios P. Lyberopoulos , Nikolaos D. Macheras

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.

Keywords

poisson processes martingale theory point processes

Cite

@article{arxiv.1905.07629,
  title  = {A characterization of martingale-equivalent compound mixed Poisson process},
  author = {Demetrios P. Lyberopoulos and Nikolaos D. Macheras},
  journal= {arXiv preprint arXiv:1905.07629},
  year   = {2019}
}

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28 pages including an appendix

A characterization of martingale-equivalent compound mixed Poisson process

Abstract

Keywords

Cite

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