EconPapers    
Economics at your fingertips  
 

A scale function based approach for solving integral-differential equations in insurance risk models

Aili Zhang, Shuanming Li and Wenyuan Wang

Applied Mathematics and Computation, 2023, vol. 450, issue C

Abstract: In risk theory, the resolutions of many interesting problems are reduced to solving some integro-differential equations (IDE), see [4, 5, 6, 7, 8, 9, 10, 12, 13, 14, 15, 21, 22, 23, 24, 25, 26, 27, 29, 31], and references therein. Meanwhile, due to the recent advances made on Lévy processes, explicit analytical expressions of the scale functions associated with Lévy processes become on offer (see [1, 2, 11, 16, 17], Chapter 8 of [19], [20], etc). This paper aims at bridging together the scale functions and the IDEs by presenting a unified scale function based approach for solving IDEs that arise in risk theory. In particular, to demonstrate the effectiveness of this approach, a dividend and capital injection problem is considered under a jump-diffusion risk model. We first derive the IDEs satisfied by the expected accumulated discounted difference between the net dividends and the costs of capital injections, and then solve the IDEs with its solution being expressed in compact and transparent forms.

Keywords: Integro-differential equation; Scale functions; Lévy process (search for similar items in EconPapers)
Date: 2023
References: View references in EconPapers View complete reference list from CitEc
Citations:

Downloads: (external link)
http://www.sciencedirect.com/science/article/pii/S0096300323001340
Full text for ScienceDirect subscribers only

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:eee:apmaco:v:450:y:2023:i:c:s0096300323001340

DOI: 10.1016/j.amc.2023.127965

Access Statistics for this article

Applied Mathematics and Computation is currently edited by Theodore Simos

More articles in Applied Mathematics and Computation from Elsevier
Bibliographic data for series maintained by Catherine Liu ().

 
Page updated 2025-03-19
Handle: RePEc:eee:apmaco:v:450:y:2023:i:c:s0096300323001340