A Novel Approximation Method for Computing the Adjustment Coefficient of a Nonlinear Cramér-Lundberg Risk Model with Gamma Claims

Basak Gever Ekinci (), Zulfiye Hanalioglu () and Tahir Khaniyev ()
Additional contact information
Basak Gever Ekinci: University of Turkish Aeronautical Association
Zulfiye Hanalioglu: Karabuk University
Tahir Khaniyev: TOBB University of Economics and Technology

Methodology and Computing in Applied Probability, 2025, vol. 27, issue 3, 1-19

Abstract: Abstract This study considers a non-linear Cramér-Lundberg risk model and examines the adjustment coefficient $$\varvec{(r)}$$ ( r ) when the claims have gamma distribution. The linear models are not always adequate because an insurance company’s premium income does not always increase linearly. Therefore, in this study, a more realistic non-linear Cramér-Lundberg risk model is mathematically constructed. Then, the ruin probability of this non-linear risk model is studied when the premium function is in the form of square root function, i.e., $$\varvec{p}\varvec{(t)}\varvec{=}\varvec{c}\varvec{\sqrt{t}}$$ p ( t ) = c t . It leads to analyzing the adjustment coefficient $$\varvec{(r)}$$ ( r ) , as examining this coefficient is required for finding an upper bound while investigating the ruin probability. However, in general case, it is a challenging procedure to calculate the exact value of $$\varvec{r}$$ r from an integral equation. Thus, in this study, the adjustment coefficient $$\varvec{r}$$ r is explored by computational methods and a new approximate formula for the practical calculation of the adjustment coefficient is proposed. Moreover, an implementation of the obtained approximate formula, which investigates ruin probability, is included as an example at the end of the paper.

Keywords: Non-linear Cramér-Lundberg risk model; Ruin probability; Approximate formula for adjustment coefficient; Gamma distribution; 62P05; 91G60 (search for similar items in EconPapers)
Date: 2025
References: Add references at CitEc
Citations:

Downloads: (external link)
http://link.springer.com/10.1007/s11009-025-10194-2 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_s11009-025-10194-2

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

DOI: 10.1007/s11009-025-10194-2

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 ().