English

A characterization of equivalent martingale probability measures in a mixed renewal risk model with applications in Risk Theory

Probability 2024-08-02 v2

Abstract

If a given aggregate process SS is a compound mixed renewal process under a probability measure PP, we provide a characterization of all probability measures QQ on the domain of PP such that QQ and PP are progressively equivalent and SS is converted into a compound mixed Poisson process under QQ. This result extends earlier works of Delbaen & Haezendonck [2], Embrechts & Meister [5], Lyberopoulos & Macheras [11], and of the authors [14]. Implications to the ruin problem and 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

Cite

@article{arxiv.2007.09051,
  title  = {A characterization of equivalent martingale probability measures in a mixed renewal risk model with applications in Risk Theory},
  author = {Spyridon M. Tzaninis and Nikolaos D. Macheras},
  journal= {arXiv preprint arXiv:2007.09051},
  year   = {2024}
}