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Open AccessArticle

Ruin Probability Functions and Severity of Ruin as a Statistical Decision Problem

1
Department of Quantitative Methods and Institute of Tourism and Sustainable Economic Development (TIDES), University of Las Palmas de Gran Canaria, E-35017 Las Palmas de Gran Canaria, Spain
2
Department of Economics, University of Cantabria, E-39005 Santander, Spain
3
Centre for Actuarial Studies, Department of Economics, The University of Melbourne, Melbourne, VIC 3010, Australia
*
Author to whom correspondence should be addressed.
Risks 2019, 7(2), 68; https://doi.org/10.3390/risks7020068
Received: 24 May 2019 / Revised: 6 June 2019 / Accepted: 11 June 2019 / Published: 17 June 2019
(This article belongs to the Special Issue Loss Models: From Theory to Applications)
It is known that the classical ruin function under exponential claim-size distribution depends on two parameters, which are referred to as the mean claim size and the relative security loading. These parameters are assumed to be unknown and random, thus, a loss function that measures the loss sustained by a decision-maker who takes as valid a ruin function which is not correct can be considered. By using squared-error loss function and appropriate distribution function for these parameters, the issue of estimating the ruin function derives in a mixture procedure. Firstly, a bivariate distribution for mixing jointly the two parameters is considered, and second, different univariate distributions for mixing both parameters separately are examined. Consequently, a catalogue of ruin probability functions and severity of ruin, which are more flexible than the original one, are obtained. The methodology is also extended to the Pareto claim size distribution. Several numerical examples illustrate the performance of these functions. View Full-Text
Keywords: loss function; exponential distribution; pareto distribution; ruin function; severity of ruin; upper bound loss function; exponential distribution; pareto distribution; ruin function; severity of ruin; upper bound
MDPI and ACS Style

Gómez-Déniz, E.; Sarabia, J.M.; Calderín-Ojeda, E. Ruin Probability Functions and Severity of Ruin as a Statistical Decision Problem. Risks 2019, 7, 68.

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