Loss Distributions

Burnecki, Krzysztof; Misiorek, Adam; Weron, Rafał

doi:10.1007/3-540-27395-6_13

Cited by 20 publications

(14 citation statements)

References 6 publications

Supporting

Mentioning

Contrasting

Unclassified

Order By: Relevance

“…In order to confirm that the tempered stable subordinator is better than the stable one we show also the Laplace transform for the process {Y T (t)} with λ = 0 (the other parameters we estimate by using the same method as this presented in section 2). Moreover we test also the Gaussian and α−stable distributions for differenced series of DATA1 by using the methods based on the distance between empirical nad theoretical distribution functions, [44]. Those tests reject the hypothesis of the stable or Gaussian behavior of the observed data.…”

Section: Applicationsmentioning

confidence: 99%

Arithmetic Brownian motion subordinated by tempered stable and inverse tempered stable processes

Wyłomańska

2012

Physica A: Statistical Mechanics and its Applications

View full text Add to dashboard Cite

In the last decade the subordinated processes have become popular and found many practical applications. Therefore in this paper we examine two processes related to time-changed (subordinated) classical Brownian motion with drift (called arithmetic Brownian motion). The first one, so called normal tempered stable, is related to the tempered stable subordinator, while the second one -to the inverse tempered stable process. We compare the main properties (such as probability density functions, Laplace transforms, ensemble averaged mean squared displacements) of such two subordinated processes and propose the parameters' estimation procedures. Moreover we calibrate the analyzed systems to real data related to indoor air quality.

show abstract

Section: Applicationsmentioning

confidence: 99%

Arithmetic Brownian motion subordinated by tempered stable and inverse tempered stable processes

Wyłomańska

2012

Physica A: Statistical Mechanics and its Applications

View full text Add to dashboard Cite

show abstract

“…Unfortunately fitting Skew Normal or Skew t distributions on positive data using a frequentist approach, as in Eling (2012), can lead to unappealing estimates because of the unboundedness of the likelihood with respect to the skewness parameter. Moreover, as pointed out by Burnecki et al (2010), usually claims distributions show the presence of small, medium and large size claims, characteristics that are hardly compatible with the choice of fitting a single parametric analytical distribution.…”

Section: Introductionmentioning

confidence: 99%

“…Among different approaches, the analytical method consisting in estimating the unknown parameters of a given parametric family of probability distributions has been the most adopted in the actuarial literature. Since it is well recognized that the loss distribution is strongly skewed with heavy tails, different candidates for claim severity distribution have been considered in the applications: the log-Normal, the Burr, the Weibull the Gamma and the Generalized Pareto distribution in the context of Extreme Value Theory see for example McNeil (1997), Embrechts et al (1997) and Burnecki et al (2010) and references cited therein. Despite their extensive application, the theoretical properties of these distributions are not always empirically matched by observed stylized facts of insurance data.…”

Section: Introductionmentioning

confidence: 99%

Skew mixture models for loss distributions: A Bayesian approach

Bernardi

Maruotti

Petrella

2012

Insurance: Mathematics and Economics

View full text Add to dashboard Cite

The derivation of loss distribution from insurance data is a very interesting research topic but at the same time not an easy task. To find an analytic solution to the loss distribution may be mislading although this approach is frequently adopted in the actuarial literature. Moreover, it is well recognized that the loss distribution is strongly skewed with heavy tails and present small, medium and large size claims which hardly can be fitted by a single analytic and parametric distribution. Here we propose a finite mixture of Skew Normal distributions that provides a better characterization of insurance data. We adopt a Bayesian approach to estimate the model, providing the likelihood and the priors for the all unknow parameters; we implement an adaptive Markov Chain Monte Carlo algorithm to approximate the posterior distribution. We apply our approach to a well known Danish fire loss data and relevant risk measures, as Value-at-Risk and Expected Shortfall probability, are evaluated as well.

show abstract

“…The evidence for the use of Weibull distribution in Actuarial statistics is found in [1] [8]. In [8], the Weibull distribution was fitted to a small data set of hurricane losses whereas [9] have used it for modeling two illustrious set of published data namely the Danish Fire Insurance data and Property claim services data. Although, there can be other suitable models for loss modeling in General Insurance, we are primarily concerned with the Burr XII and Weibull distributions as loss models for our claim data and have concentrated on the computation of actuarial quantities like the probability of ultimate ruin through simulation and the probability function for the number of claims until ruin.…”

Section: Introductionmentioning

confidence: 99%

Modeling of Insurance Data through Two Heavy Tailed Distributions: Computations of Some of Their Actuarial Quantities through Simulation from Their Equilibrium Distributions and the Use of Their Convolutions

Nath¹,

Das²

2016

JMF

View full text Add to dashboard Cite

In this paper, we have fitted two heavy tailed distributions viz the Weibull distribution and the Burr XII distribution to a set of Motor insurance claim data. As it is known, the probability of ruin is obtained as a solution to an integro differential equation, general solution of which leads to what is known as the Pollaczek-Khinchin Formula for the probability of ultimate ruin. In case, the claim severity is distributed as the above two mentioned distributions, and Pollaczek-Khinchin formula cannot be used to evaluate the probability of ruin through inversion of their Laplace transform since the Laplace Transforms themselves don't have closed form expression. However, an approximation to the probability of ultimate ruin in such cases can be obtained by the Pollaczek-Khinchin formula through simulation and one crucial step in this simulation is to simulate from the corresponding Equilibrium distribution of the claim severity distribution. The paper lays down methodologies to simulate from the Equilibrium distribution of Burr XII distribution and Weibull distribution and has used them to obtain an approximation to the probability of ultimate ruin through Pollaczek-Khinchin formula by Monte Carlo simulation. An attempt has also been made to obtain numerical values to the probability function for the number of claims until ruin in case of zero initial surplus under these claim severity distributions and this in turn necessitates the computation of the convolutions of these distributions. The paper makes a preliminary effort to address this issue. All the computations are done under the assumption of the Classical Risk Model.

show abstract

Loss Distributions

Cited by 20 publications

References 6 publications

Arithmetic Brownian motion subordinated by tempered stable and inverse tempered stable processes

Arithmetic Brownian motion subordinated by tempered stable and inverse tempered stable processes

Skew mixture models for loss distributions: A Bayesian approach

Modeling of Insurance Data through Two Heavy Tailed Distributions: Computations of Some of Their Actuarial Quantities through Simulation from Their Equilibrium Distributions and the Use of Their Convolutions

Contact Info

Product

Resources

About