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

Abstract

If a given aggregate process $S$ is a compound mixed renewal process under a probability measure $P$, we provide a characterization of all probability measures $Q$ on the domain of $P$ such that $Q$ and $P$ are progressively equivalent and $S$ is converted into a compound mixed Poisson process under $Q$. 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.

References in corpus (2)

• A characterization of equivalent martingale measures in a renewal risk model with applications to premium calculation principles
• A characterization of martingale-equivalent compound mixed Poisson process