On Defective Renewal Equations and Compound Geometric Distributions, with Applications in Ruin Theory

Stathis Chadjiconstantinidis () and Georgios Psarrakos ()
Additional contact information
Stathis Chadjiconstantinidis: University of Piraeus
Georgios Psarrakos: University of Piraeus

Methodology and Computing in Applied Probability, 2025, vol. 27, issue 3, 1-30

Abstract: Abstract In this paper, by using a Weyl-type operator, the notion of the n-th order equilibrium function of a given function is introduced and higher-order equilibrium properties for the solution of a defective renewal equation are studied. It is shown that the n-th order equilibrium of such solution also satisfies a defective renewal equation. Furthermore, convolution representations for these functions are given. Several applications for compound geometric distributions and for convolutions involving a compound geometric distribution are studied. Further expressions for functions with interest in ruin theory are obtained, as well as mixture representations. Finally, some bounds and applications are also provided to the classical risk model.

Keywords: Defective renewal equation; Equilibrium distribution; Stop-loss transform; Weyl operator; Residual lifetime; Aging classes; Ruin theory; Primary 60E05; Secondary 91G05 (search for similar items in EconPapers)
Date: 2025
References: Add references at CitEc
Citations:

Downloads: (external link)
http://link.springer.com/10.1007/s11009-025-10178-2 Abstract (text/html)
Access to the full text of the articles in this series is restricted.

Related works:
This item may be available elsewhere in EconPapers: Search for items with the same title.

Export reference: BibTeX RIS (EndNote, ProCite, RefMan) HTML/Text

Persistent link: https://EconPapers.repec.org/RePEc:spr:metcap:v:27:y:2025:i:3:d:10.1007_s11009-025-10178-2

Ordering information: This journal article can be ordered from
https://www.springer.com/journal/11009

DOI: 10.1007/s11009-025-10178-2

Access Statistics for this article

Methodology and Computing in Applied Probability is currently edited by Joseph Glaz

More articles in Methodology and Computing in Applied Probability from Springer
Bibliographic data for series maintained by Sonal Shukla () and Springer Nature Abstracting and Indexing ().