A note on some joint distribution functions involving the time of ruin

In a recent paper, Willmot (2015) derived an expression for the joint distribution function of the time of ruin and the deficit at ruin in the classical risk model. We show how his approach can be applied to obtain a simpler expression, and by interpreting this expression by probabilistic reasoning...

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Bibliographic Details
Published inInsurance, mathematics & economics Vol. 67; pp. 120 - 124
Main Author Dickson, David C.M.
Format Journal Article
LanguageEnglish
Published Amsterdam Elsevier B.V 01.03.2016
Elsevier Sequoia S.A
Subjects
Deficit at ruin
Joint distribution function
MAP risk model
Mathematical functions
Mathematical models
Mathematical problems
Probability distribution
Risk assessment
Studies
Surplus prior to ruin
Time of ruin
Time of ruin
Deficit at ruin
Surplus prior to ruin
Joint distribution function
MAP risk model
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Summary:In a recent paper, Willmot (2015) derived an expression for the joint distribution function of the time of ruin and the deficit at ruin in the classical risk model. We show how his approach can be applied to obtain a simpler expression, and by interpreting this expression by probabilistic reasoning we obtain solutions for more general risk models. We also discuss how some of Willmot’s results relate to existing literature on the probability and severity of ruin.
ISSN:0167-6687
1873-5959
DOI:10.1016/j.insmatheco.2015.12.005