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On a class of renewal risk model with random income
Author(s) -
Yang Hu,
Zhang Zhimin
Publication year - 2008
Publication title -
applied stochastic models in business and industry
Language(s) - English
Resource type - Journals
SCImago Journal Rank - 0.413
H-Index - 40
eISSN - 1526-4025
pISSN - 1524-1904
DOI - 10.1002/asmb.752
Subject(s) - laplace transform , expression (computer science) , penalty method , mathematics , poisson distribution , function (biology) , class (philosophy) , order (exchange) , compound poisson process , closed form expression , risk model , distribution (mathematics) , renewal theory , poisson process , combinatorics , mathematical economics , mathematical optimization , mathematical analysis , statistics , economics , computer science , finance , programming language , evolutionary biology , artificial intelligence , biology
In this paper, we consider a renewal risk process with random premium income based on a Poisson process. Generating function for the discounted penalty function is obtained. We show that the discounted penalty function satisfies a defective renewal equation and the corresponding explicit expression can be obtained via a compound geometric tail. Finally, we consider the Laplace transform of the time to ruin, and derive the closed‐form expression for it when the claims have a discrete K m distribution (i.e. the generating function of the distribution function is a ratio of two polynomials of order m ∈ℕ + ). Copyright © 2008 John Wiley & Sons, Ltd.