Bayesian Modelling of Outstanding Liabilities Incorporating Claim Count Uncertainty

Ntzoufras, Ioannis; Δελλαπόρτας, Πέτρος

doi:10.1080/10920277.2002.10596032

Cited by 61 publications

(69 citation statements)

References 46 publications

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“…Nevertheless, it is possible that the effect of any variable could suffer changes across the years, and this aspect is not included in the previous estimates. For this reason, we take a standard multinomial model as the base one, which follows the approach and notations of Ntzoufras (2009). As we are dealing with time series, it may be reasonable to consider the existence of some kind of autocorrelation in data.…”

Section: Models To Evaluate the Classification And Empirical Evidencementioning

confidence: 99%

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Some criticism to a general model in Solvency II: an explanation from a clustering point of view

2016

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It is a well-known fact that heterogeneity is one of the characteristics of the insurance market, and it is relevant to classify and characterize companies by means of their financial properties and different risk profiles. So, it may not be adequate to use a general model for all the companies operating in the European market, as the one proposed by the Directive 2009/138/CE. Solvency II is a general regulatory model such that the volume of own resources will be determined depending on risks based on a calibration reached considering the average behaviour of companies. In order to criticize this approach, we have obtained a characterization of the profiles of companies using a PAM clustering methodology, adapted for longitudinal data, and we have studied the evolution of the obtained groups of companies under a Bayesian approach. In this way, we have introduced a multinomial general dynamic linear model to study the probabilities of the companies to be included into each group. The characterization and identification of these groups suggest that an unique regulatory model may be unsuitable. We have used data from DGSFP (Spanish insurance regulator), with public information about the balance sheets and income statements from years 1999 to 2011.

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Section: Models To Evaluate the Classification And Empirical Evidencementioning

confidence: 99%

“…The restriction η ti1 = 0 can be indirectly imposed by setting all coefficients of the first linear predictor β ti1 equal to zero (see Ntzoufras 2009). With regard to the autoregressive relation between parameters, it can be modelled as:…”

Section: Models To Evaluate the Classification And Empirical Evidencementioning

confidence: 99%

Some criticism to a general model in Solvency II: an explanation from a clustering point of view

2016

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“…The models in the papers of the first category are mostly distribution-free in contrast to the papers of the second category (Verrall (1989(Verrall ( ,1994, Ntzoufras and Dellaportas (2002)), in which incremental payments are assumed to follow a log-normal distribution. The logarithmic incremental payments are specified by the log-normal model:…”

Section: Modeling Of Claims Development Datamentioning

confidence: 99%

“…The accident and development year parameters are further assumed to evolve as follows for the same reasons as in De Jong and Zehnwirth (1983): (5) was also named as the "linear CL model" by Verrall (1989Verrall ( ,1994, since it is very similar to an additive representation of the CL method (see also Kremer (1982)). In addition to the basic model (5), which is used by Verrall (1989) and Li (2006), Verrall (1994) and Ntzoufras and Dellaportas (2002) extend the basic model by integrating varying run-off evolutions.…”

Section: Modeling Of Claims Development Datamentioning

confidence: 99%

State Space Models and the Kalman-Filter in Stochastic Claims Reserving: Forecasting, Filtering and Smoothing

Chukhrova

Johannssen

2017

Risks

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This paper gives a detailed overview of the current state of research in relation to the use of state space models and the KALMAN-filter in the field of stochastic claims reserving. Most of these state space representations are matrix-based, which complicates their applications. Therefore, to facilitate the implementation of state space models in practice, we present a scalar state space model for cumulative payments, which is an extension of the well-known chain ladder (CL) method. The presented model is distribution-free, forms a basis for determining the entire unobservable lower and upper run-off triangles and can easily be applied in practice using the KALMAN-filter for prediction, filtering and smoothing of cumulative payments. In addition, the model provides an easy way to find outliers in the data and to determine outlier effects. Finally, an empirical comparison of the scalar state space model, promising prior state space models and some popular stochastic claims reserving methods is performed.

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“…Zhang et al (2012) propose a Bayesian non linear hierarchical model with growth curves to model the loss development process, using data from individual companies forming various cohorts of claims. Ntzoufras and Dellaportas (2002) investigate various models for outstanding claims problems using a Bayesian approach via Markov chain Monte Carlo (MCMC) sampling strategy and show that the computational flexibility of a Bayesian approach facilitated the implementation of complex models.…”

Section: Background On Risk Margin Calculationmentioning

confidence: 99%

Risk Margin Quantile Function via Parametric and Non-Parametric Bayesian Quantile Regression

2014

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We develop quantile regression models in order to derive risk margin and to evaluate capital in non-life insurance applications. By utilizing the entire range of conditional quantile functions, especially higher quantile levels, we detail how quantile regression is capable of providing an accurate estimation of risk margin and an overview of implied capital based on the historical volatility of a general insurers loss portfolio. Two modelling frameworks are considered based around parametric and nonparametric quantile regression models which we develop specifically in this insurance setting.In the parametric quantile regression framework, several models including the flexible generalized beta distribution family, asymmetric Laplace (AL) distribution and power Pareto distribution are considered under a Bayesian regression framework. The Bayesian posterior quantile regression models in each case are studied via Markov chain Monte Carlo (MCMC) sampling strategies.In the nonparametric quantile regression framework, that we contrast to the parametric Bayesian models, we adopted an AL distribution as a proxy and together with the parametric AL model, we expressed the solution as a scale mixture of uniform distributions to facilitate implementation. The models are extended to adopt dynamic mean, variance and skewness and applied to analyze two real loss reserve data sets to perform inference and discuss interesting features of quantile regression for risk margin calculations.Asymmetric Laplace distribution, Bayesian inference, Markov chain Monte Carlo methods, Quantile regression, loss reserve, risk margin, central estimate.

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Bayesian Modelling of Outstanding Liabilities Incorporating Claim Count Uncertainty

Cited by 61 publications

References 46 publications

Some criticism to a general model in Solvency II: an explanation from a clustering point of view

Some criticism to a general model in Solvency II: an explanation from a clustering point of view

State Space Models and the Kalman-Filter in Stochastic Claims Reserving: Forecasting, Filtering and Smoothing

Risk Margin Quantile Function via Parametric and Non-Parametric Bayesian Quantile Regression

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