arXiv subjects

Apostolos Bozikas

Publications and source records attributed to Apostolos Bozikas.

3 recordsLinked to original sources

arXiv2026

A characterization of ruin-inducing probability measures in a renewal risk model

In this work, we derive a complete characterization of all ruin-inducing probability measures that preserve the structure of a given compound renewal process in terms of suitable pairs of functions $(γ,δ)$. This result allows us to obtain an explicit representation of the infinite-time ruin probability as an expectation under any ruin-inducing probability measure. A key feature of our approach is that the construction of these measures does not rely on the existence of moment generating functions, and is therefore applicable to heavy-tailed claim size distributions. The proposed framework includes the classical Esscher transform as a special case.

math.PR↗

arXiv2026

On the cumulative residual interval entropy of doubly truncated random variables

This paper introduces and studies a new uncertainty measure, the cumulative residual interval entropy (CRIE). Defined as the cumulative residual entropy of a doubly truncated (interval) continuous random variable, this measure has several applications when data fall between two points. The CRIE generalizes the cumulative residual entropy proposed by Rao et al. [31] and the dynamic cumulative residual entropy proposed by Asadi and Zohrevand [1]. We establish some properties of the generalized hazard rate and the doubly truncated mean residual lifetime, which are useful for obtaining results for the CRIE. Furthermore, we provide several representations of the CRIE based on reliability measures, covariance, the relevation transform, and increasing transformations. Finally, upper and lower bounds, as well as monotonicity results for the CRIE, are provided.

math.PR↗

arXiv2024

Extensions of Panjer's recursion for mixed compound distributions

In actuarial practice, the usual independence assumptions for the collective risk model are often violated, implying a growing need for considering more general models that incorporate dependence. To this purpose, the present paper studies the mixed counterpart of the classical Panjer family of claim number distributions and their compound version, by allowing the parameters of the distributions to be viewed as random variables. Under the assumptions that the claim size process is conditionally i.i.d. and (conditionally) mutually independent of the claim counts, we provide a recursive algorithm for the computation of the probability mass function of the aggregate claim sizes. The case of a compound Panjer distribution with exchangeable claim sizes is also studied. For the sake of completeness, our results are illustrated by various numerical examples.

math.PR↗