scholarly journals Heavy-Tailed Distributions and Rating

2001 ◽  
Vol 31 (1) ◽  
pp. 37-58 ◽  
Author(s):  
J. Beirlant ◽  
G. Matthys ◽  
G. Dierckx
Keyword(s):  
Parametric Model ◽  
Extreme Value ◽  
Small Sample ◽  
Data Set ◽  
Large Claim ◽  
Heavy Tailed Distributions ◽  
Fire Insurance ◽  
Insurance Portfolio ◽  
Claim Size Distribution ◽  
Heavy Tailed

AbstractIn this paper we consider the problem raised in the Astin Bulletin (1999) by Prof. Benktander at the occasion of his 80th birthday concerning the choice of an appropriate claim size distribution in connection with reinsurance rating problems. Appropriate models for large claim distributions play a central role in this matter. We review the literature on extreme value methodology and consider its use in reinsurance. Whereas the models in extreme-value methods are non-parametric or semi-parametric of nature, practitioners often need a fully parametric model for assessing a portfolio risk both in the tails and in more central portions of the claim distribution. To this end we propose a parametric model, termed the generalised Burr-gamma distribution, which possesses such flexibility. Throughout we consider a Norwegian fire insurance portfolio data set in order to illustrate the concepts. A small sample simulation study is performed to validate the different methods for estimating excess-of-loss reinsurance premiums.

scholarly journals Finite-time ruin probabilities under large-claim reinsurance treaties for heavy-tailed claim sizes

2020 ◽  
Vol 57 (2) ◽  
pp. 513-530
Author(s):  
Hansjörg Albrecher ◽  
Bohan Chen ◽  
Eleni Vatamidou ◽  
Bert Zwart
Keyword(s):  
Finite Time ◽  
Heavy Tails ◽  
Asymptotic Expression ◽  
Sample Path ◽  
Rare Event ◽  
Large Claim ◽  
Simulation Techniques ◽  
Insurance Portfolio ◽  
Regularly Varying ◽  
Heavy Tailed

AbstractWe investigate the probability that an insurance portfolio gets ruined within a finite time period under the assumption that the r largest claims are (partly) reinsured. We show that for regularly varying claim sizes the probability of ruin after reinsurance is also regularly varying in terms of the initial capital, and derive an explicit asymptotic expression for the latter. We establish this result by leveraging recent developments on sample-path large deviations for heavy tails. Our results allow, on the asymptotic level, for an explicit comparison between two well-known large-claim reinsurance contracts, namely LCR and ECOMOR. Finally, we assess the accuracy of the resulting approximations using state-of-the-art rare event simulation techniques.

MODELLING INSURANCE DATA WITH THE PARETO ARCTAN DISTRIBUTION

2015 ◽  
Vol 45 (3) ◽  
pp. 639-660 ◽  
Author(s):  
Emilio Gómez-Déniz ◽  
Enrique Calderín-Ojeda
Keyword(s):  
Scale Parameter ◽  
Survival Function ◽  
Inverse Gamma ◽  
Heavy Tailed Distributions ◽  
Fire Insurance ◽  
Tangent Function ◽  
Heavy Tailed ◽  
Limiting Case ◽  
Insurance Data ◽  
Theoretical Results

AbstractIn this paper, a new methodology based on the use of the inverse of the circular tangent function that allows us to add a scale parameter (say α) to an initial survival function is presented. The latter survival function is determined as limiting case when α tends to zero. By choosing as parent the classical Pareto survival function, the Pareto ArcTan (PAT) distribution is obtained. After providing a comprehensive analysis of its statistical properties, theoretical results with reference to insurance are illustrated. Its performance is compared, by means of the well-known Norwegian fire insurance data, with other existing heavy-tailed distributions in the literature such as Pareto, Stoppa, Shifted Lognormal, Inverse Gamma and Fréchet distributions.

Using Extreme Value Theory to Model Electricity Price Risk with an Application to the Alberta Power Market

2005 ◽  
Vol 23 (5) ◽  
pp. 375-403 ◽  
Author(s):  
W. D. Walls ◽  
Wei. Zhang
Keyword(s):  
Extreme Value Theory ◽  
Value At Risk ◽  
Generalized Pareto Distribution ◽  
Value Theory ◽  
Extreme Value ◽  
Financial Assets ◽  
Historical Simulation ◽  
Generalized Pareto ◽  
Heavy Tailed Distributions ◽  
Heavy Tailed

Value-at-risk (VaR) is a measure of the maximum potential change in value of a portfolio of financial assets with a given probability over a given time horizon. VaR has become a standard measure of market risk and a common practice is to compute VaR by assuming that changes in value of the portfolio are conditionally normally distributed. However, assets returns usually come from heavy-tailed distributions, so computing VaR under the assumption of conditional normality can be an important source of error. We illustrate in our application to competitive electric power prices in Alberta, Canada, that VaR estimates based on extreme value theory models, in particular the generalized Pareto distribution are, more accurate than those produced by alternative models such as normality or historical simulation.

Box–Cox transformations and heavy-tailed distributions

2004 ◽  
Vol 41 (A) ◽  
pp. 213-227 ◽  
Author(s):  
Jef L. Teugels ◽  
Giovanni Vanroelen
Keyword(s):  
Statistical Analysis ◽  
Extreme Value Theory ◽  
Value Theory ◽  
Extreme Value ◽  
Theoretical Background ◽  
Graphical Representations ◽  
Heavy Tailed Distributions ◽  
Heavy Tailed ◽  
Box Cox Transformation

It is a stylized fact that estimators in extreme-value theory suffer from serious bias. Moreover, graphical representations of extremal data often show erratic behaviour. In the statistical literature it is advised to use a Box–Cox transformation in order to make data more suitable for statistical analysis. We provide some of the theoretical background to see the effect of such transformations and to investigate under what circumstances they might be helpful.

Box–Cox transformations and heavy-tailed distributions

2004 ◽  
Vol 41 (A) ◽  
pp. 213-227 ◽  
Author(s):  
Jef L. Teugels ◽  
Giovanni Vanroelen
Keyword(s):  
Statistical Analysis ◽  
Extreme Value Theory ◽  
Value Theory ◽  
Extreme Value ◽  
Theoretical Background ◽  
Graphical Representations ◽  
Heavy Tailed Distributions ◽  
Heavy Tailed ◽  
Box Cox Transformation

It is a stylized fact that estimators in extreme-value theory suffer from serious bias. Moreover, graphical representations of extremal data often show erratic behaviour. In the statistical literature it is advised to use a Box–Cox transformation in order to make data more suitable for statistical analysis. We provide some of the theoretical background to see the effect of such transformations and to investigate under what circumstances they might be helpful.

scholarly journals Improved Estimator of the Conditional Tail Expectation in the case of heavy-tailed losses

2020 ◽  
Vol 8 (1) ◽  
pp. 98-109
Author(s):  
Mohamed Laidi ◽  
Abdelaziz Rassoul ◽  
Hamid Ould Rouis
Keyword(s):  
Asymptotic Normality ◽  
Simulation Study ◽  
Mean Squared Error ◽  
Extreme Value ◽  
Loss Distribution ◽  
Squared Error ◽  
Heavy Tailed Distributions ◽  
High Quantile ◽  
Heavy Tailed ◽  
Conditional Tail Expectation

In this paper, we investigate the extreme-value methodology, to propose an improved estimator of the conditional tail expectation (CTE) for a loss distribution with a finite mean but infinite variance.The present work introduces a new estimator of the CTE based on the bias-reduced estimators of high quantile for heavy-tailed distributions. The asymptotic normality of the proposed estimator is established and checked, in a simulation study. Moreover, we compare, in terms of bias and mean squared error, our estimator with the known old estimator.

The Impact of Green Labels on U.S. Hotel Net Operating Income: Operating Statements Analyses

2019 ◽  
Vol 11 (1) ◽  
pp. 156-173
Author(s):  
Spenser Robinson ◽  
A.J. Singh
Keyword(s):  
Environmental Design ◽  
Green Buildings ◽  
Small Sample ◽  
Sample Survey ◽  
Data Set ◽  
Operating Income ◽  
Energy Star ◽  
The Impact ◽  
Industry Professionals

This paper shows Leadership in Energy and Environmental Design (LEED) certified hospitality properties exhibit increased expenses and earn lower net operating income (NOI) than non-certified buildings. ENERGY STAR certified properties demonstrate lower overall expenses than non-certified buildings with statistically neutral NOI effects. Using a custom sample of all green buildings and their competitive data set as of 2013 provided by Smith Travel Research (STR), the paper documents potential reasons for this result including increased operational expenses, potential confusion with certified and registered LEED projects in the data, and qualitative input. The qualitative input comes from a small sample survey of five industry professionals. The paper provides one of the only analyses on operating efficiencies with LEED and ENERGY STAR hospitality properties.

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