SOME COMPOSITE MODELS AND THEIR APPLICATION TO TURKISH MOTOR INSURANCE DATA

Yıl 2019, Cilt: 7 Sayı: 2, 121 - 132, 23.08.2019

Ayten Yiğiter Yasemin Gençtürk Canan Hamurkaroğlu

https://doi.org/10.20290/estubtdb.609469

Öz

It is important for an
insurance company to predict the future claims in order to evaluate premiums,
to determine the reserve necessary to meet its obligation and probabilities of
ruin, etc. as the claim data is highly positively skewed and has heavy tail, no
standard parametric model seems to provide an acceptable fit to both small and
large losses. Composite models that use one standard distribution up to a
threshold and other standard distribution thereafter are developed and it is seen
that these composite models provide better fit than the standard models when
claim data involve small and high claims.

 

The aim of this study is to
investigate the use of the composite models namely Exponential-Pareto,
Weibull-Pareto and Lognormal-Pareto to model the Turkish Motor Insurance claim
data. From the results obtained, it is concluded that the composite
Weibull-Pareto model provides better fit to Turkish Motor Insurance claim data
than the all other models considered.

Anahtar Kelimeler

Composite models, Standard parametric models, Turkish motor insurance loss data

Kaynakça

• [1] Cooray K, Ananda MMA. Modeling Actuarial Data with a Composite Lognormal-Pareto Model. Scandinavian Actuarial Journal 2005; 5: 321-334.
• [2] Ciumara R. An Actuarial Model Based on Composite Weibull-Pareto Distribution. Mathematical Report-Bucharest 2006; 8 (4): 401-411.
• [3] Preda V, Ciumara R. On Composite Models: Weibull-Pareto and Lognormal-Pareto: A Comparative Study. Romanian Journal of Economic Forecasting 2006; 2: 32-46.
• [4] Teodorescu S, Vernic R. A Composite Exponential-Pareto Distribution. An. Şt. Univ. Ovidius Constanta 2006; 14(1): 99-108.
• [5] Scollnik DPM. On Composite Lognormal-ParetoModels. Scandinavian Actuarial Journal 2007; 1: 20-33.
• [6] Teodorescu S, Vernic R. Some Composite Exponential-Pareto Models for Actuarial Prediction. Romanian Journal of Economic Forecasting 2009; 4: 82-100.
• [7] Vernic R, Teodorescu S, Pelican E. Two Lognormal Models for Real Data. An. Şt. Univ. Ovidius Constanta 2009; 17(3): 263-279.
• [8] Nadarajah S, Bakar SAA. New composite Models for the Danish Fire Insurance Data. Scandinavian Actuarial Journal 2014; 2014(2): 180-187.
• [9] Maghsoudi M, Abu Bakar S. A, Hamzah NA. Composite Weibull-Inverse Transformed Gamma Distribution and Its Actuarial Application, Proceedings of the 21st National Symposium on Mathematical Sciences 2014.
• [10] Calderin-Ojeda E, Kwok CF. Modelling Large Claims with Composite Stoppa Models. Scandinavian Actuarial Journal 2015, Available from http://dx.doi.org/10.1080/03461238.2015.1034763.
• [11] Abu Bakar SA, Hamzah NA, Maghsoudi M. Nadarajah S. Modelling Loss Data Using Composite Models. Insurance: Mathematics and Economics 2015; 61: 146-154.
• [12] Klugman SS, Panjer HH, Willmot GE. Loss Models From Data to Decisions, New York: John Wiley&Sons, Inc., 1998.