On the analysis of ruin-related quantities in the delayed renewal risk model
| Autor: | Gordon E. Willmot, So-Yeun Kim |
|---|---|
| Rok vydání: | 2016 |
| Předmět: |
Statistics and Probability
Economics and Econometrics Laplace transform 010102 general mathematics Function (mathematics) Ruin theory Residual 01 natural sciences 010104 statistics & probability Risk model Applied mathematics Renewal equation 0101 mathematics Statistics Probability and Uncertainty First-hitting-time model Residual time Mathematical economics Mathematics |
| Zdroj: | Insurance: Mathematics and Economics. 66:77-85 |
| ISSN: | 0167-6687 |
| DOI: | 10.1016/j.insmatheco.2015.10.011 |
| Popis: | This paper first explores the Laplace transform of the time of ruin in the delayed renewal risk model. We show that G δ d ( u ) , the Laplace transform of the time of ruin in the delayed model, also satisfies a defective renewal equation and use this to study the Cramer–Lundberg asymptotics and bounds of G δ d ( u ) . Next, the paper considers the stochastic decomposition of the residual lifetime of maximal aggregate loss and more generally L δ d in the delayed renewal risk model, using the framework equation introduced in Kim and Willmot (2011) and the defective renewal equation for the Laplace transform of the time of ruin. As a result of the decomposition, we propose a way to calculate the mean and the moments of the proper deficit in the delayed renewal risk model. Lastly, closed form expressions are derived for the Gerber–Shiu function in the delayed renewal risk model with the distributional assumption of time until the first claim and simulation results are included to assess the impact of different distributional assumptions on the time until the first claim. |
| Databáze: | OpenAIRE |
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