Open AccessGerber-Shiu Function in a Discrete-time Risk Model with Dividend Strategy
Author(s) -
Junqing Huang,
Bao Zhang
Publication year - 2021
Publication title -
asian journal of probability and statistics
Language(s) - English
Resource type - Journals
ISSN - 2582-0230
DOI - 10.9734/ajpas/2021/v15i430367
Subject(s) - dividend , generalization , constant (computer programming) , mathematics , risk model , penalty method , function (biology) , discrete time and continuous time , mathematical economics , econometrics , mathematical optimization , economics , computer science , mathematical analysis , statistics , finance , evolutionary biology , biology , programming language
In this paper, a discrete-time risk model with dividend strategy and a general premium rate is considered. Under such a strategy, once the insurer’s surplus hits a constant dividend barrier , dividends are paid off to shareholders at instantly. Using the roots of a generalization of Lundberg’s fundamental equation and the general theory on difference equations, two difference equations for the Gerber-Shiu discounted penalty function are derived and solved. The analytic results obtained are utilized to derive the probability of ultimate ruin when the claim sizes is a mixture of two geometric distributions. Numerical examples are also given to illustrate the applicability of the results obtained.