English

A characterization of progressively equivalent probability measures preserving the structure of a compound mixed renewal process

Probability 2020-07-16 v2 Mathematical Finance

Abstract

Generalizing earlier works of Delbaen & Haezendonck [5] as well as of [18] and [16] for given compound mixed renewal process S under a probability measure P, we characterize all those probability measures Q on the domain of P such that Q and P are progressively equivalent and S remains a compound mixed renewal process under Q with improved properties. As a consequence, we prove that any compound mixed renewal process can be converted into a compound mixed Poisson process through a change of measures. Applications related to the ruin problem and to the computation of premium calculation principles in an insurance market without arbitrage opportunities are discussed in [26] and [27], respectively.

Keywords

Cite

@article{arxiv.2007.05289,
  title  = {A characterization of progressively equivalent probability measures preserving the structure of a compound mixed renewal process},
  author = {Spyridon M. Tzaninis and Nikolaos D. Macheras},
  journal= {arXiv preprint arXiv:2007.05289},
  year   = {2020}
}