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Granular loss models in reserving
Bílková, Kristýna ; Pešta, Michal (advisor) ; Mazurová, Lucie (referee)
Claims reserving methods usually use data aggregated into development triangles, therefore a lot of information that insurance companies possess remains unused. This thesis shows a triangle-free approach using granular information from a claim by claim database. A statistical model for claims development which can further be used for estimation of reserves is built. The statistical model consists of a counting process that drives claims occurrence, distribution of reporting delay and distribution of claims severity. Several suitable distributions are presented, as well as methods for obtaining their parameters from data. Theoretical apparatus is used for real data. The thesis also pursues comparison of the IBNR reserve estimation using the triangle free approach and distribution free Chain ladder method for real data as well as for simulated data sets. For the data used in this thesis the complexity and data requirements of the triangle free approach are in favor of more preciseness and versatility. Powered by TCPDF (www.tcpdf.org)
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Prediction error in non-life claims reserves
Divišová, Kateřina ; Justová, Iva (advisor) ; Mandl, Petr (referee)
This thesis deals with a description of three claims reserving methods - with stochastic models for Chain ladder, Bornhuetter/Ferguson and multiplicative method. There are mentioned their assumptions, parameter estimates, their properties and formulas for loss reserves in the first part. The second part of the text is devoted to formulas for the mean squared error of prediction and its estimate. Finally, a numerical example shows comparison of these methods.
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Munich chain ladder method
Janáková, Veronika ; Pleška, Martin (advisor) ; Jedlička, Petr (referee)
Title: Munich chain ladder method Author: Bc. Veronika Janáková Department: Department of probability and mathematical statistic Supervisor: Mgr. Martin Pleška Supervisor's e-mail address: martin.pleska@cz.pwc.com Abstract: The insurance company is obliged to create technical reserves to cover the risk from insurance activities. One of the main reserves in non-life insurance is the IBNR reserve - the reserve to cover the damages that already exist, but that have not been reported to the insurance company yet. The content and the general aim of this thesis is to provide a better orientation in the method used in the estimation of the reserve IBNR - the Munich Chain Ladder Method. Munich Chain Ladder Method was created as a modification of the standard Chain Ladder calculation - one of the most used methods in the estimation of the IBNR reserve. The thesis focuses on the reasons that led to the modification of standard Chain Ladder calculation and explains the calculation of the modified method. It presents the application ot the method on the real data as well as the comparison with the results of the classical and less complicated Chain Ladder method. Keywords: IBNR reserve, chain ladder, Munich chain ladder 1
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Stochastic claims reserving with double chain ladder
Javůrková, Tereza ; Pešta, Michal (advisor) ; Zichová, Jitka (referee)
This thesis deals with an important problem of insurance which is forecasting outstanding claims liabilities. It describes the Chain-Ladder method, the basic method for forecasting outstanding claims, and then it's extention to Double Chain-Ladder method. It also uses the number of reported claims for a beter estimate. The final forecast is calculated from the IBNR and RBNS reserves which are estimated separetly. Finly we aplly those methods to a real life dataset. The results shows differences betwen those two methods and different ways of programming. 1
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Claims reserve volatility and bootstrap with aplication on historical data with trend in claims development
Malíková, Kateřina ; Pešta, Michal (advisor) ; Zichová, Jitka (referee)
This thesis deals with the application of stochastic claims reserving methods to given data with some trends in claims development. It describes the chain ladder method and the generalized linear models as its stochastic framework. Some simple functions are suggested for smoothing the origin and development period coefficients from the estimated model. The extrapolation is also considered for estimation of the unobserved tail values. The residual bootstrap is used for the reparameterized model in order to get the predictive distribution of the estimated reserve together with its standard deviation as a measure of volatility. Solvency capital requirement in one year time horizon is also calculated. 1
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Granular loss models in reserving
Bílková, Kristýna ; Pešta, Michal (advisor) ; Mazurová, Lucie (referee)
Claims reserving methods usually use data aggregated into development triangles, therefore a lot of information that insurance companies possess remains unused. This thesis shows a triangle-free approach using granular information from a claim by claim database. A statistical model for claims development which can further be used for estimation of reserves is built. The statistical model consists of a counting process that drives claims occurrence, distribution of reporting delay and distribution of claims severity. Several suitable distributions are presented, as well as methods for obtaining their parameters from data. Theoretical apparatus is used for real data. The thesis also pursues comparison of the IBNR reserve estimation using the triangle free approach and distribution free Chain ladder method for real data as well as for simulated data sets. For the data used in this thesis the complexity and data requirements of the triangle free approach are in favor of more preciseness and versatility. Powered by TCPDF (www.tcpdf.org)
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Double chain ladder
Perichtová, Margaréta ; Pešta, Michal (advisor) ; Mazurová, Lucie (referee)
This thesis deals with one of the biggest problems in non-life insurance and that is forecasting outstanding claims liabilities. Chain ladder method is probably the most often used method for estimating outstanding liabilities. Firstly, we show classic chain ladder method and its deterministic and stochastic form. Secondly, we introduce relatively new method, double chain ladder method which comes from chain ladder method, but in addition it considers number of reported claims, that allow us to count RBNS reserve more precisely and also to count IBNR and RBNS reserves separately. In the end we apply both methods on the real data. We compute point estimate of the reserve by chain ladder method and by double chain ladder method and compare the results. Powered by TCPDF (www.tcpdf.org)
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Prediction error in non-life claims reserves
Divišová, Kateřina ; Justová, Iva (advisor) ; Mandl, Petr (referee)
This thesis deals with a description of three claims reserving methods - with stochastic models for Chain ladder, Bornhuetter/Ferguson and multiplicative method. There are mentioned their assumptions, parameter estimates, their properties and formulas for loss reserves in the first part. The second part of the text is devoted to formulas for the mean squared error of prediction and its estimate. Finally, a numerical example shows comparison of these methods.
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Munich chain ladder method
Janáková, Veronika ; Pleška, Martin (advisor) ; Jedlička, Petr (referee)
Title: Munich chain ladder method Author: Bc. Veronika Janáková Department: Department of probability and mathematical statistic Supervisor: Mgr. Martin Pleška Supervisor's e-mail address: martin.pleska@cz.pwc.com Abstract: The insurance company is obliged to create technical reserves to cover the risk from insurance activities. One of the main reserves in non-life insurance is the IBNR reserve - the reserve to cover the damages that already exist, but that have not been reported to the insurance company yet. The content and the general aim of this thesis is to provide a better orientation in the method used in the estimation of the reserve IBNR - the Munich Chain Ladder Method. Munich Chain Ladder Method was created as a modification of the standard Chain Ladder calculation - one of the most used methods in the estimation of the IBNR reserve. The thesis focuses on the reasons that led to the modification of standard Chain Ladder calculation and explains the calculation of the modified method. It presents the application ot the method on the real data as well as the comparison with the results of the classical and less complicated Chain Ladder method. Keywords: IBNR reserve, chain ladder, Munich chain ladder 1
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The stochastical approaches to the claims reserving
Hronová, Lucie ; Witzany, Jiří (advisor) ; Kolman, Marek (referee)
The subject matter of this master thesis is the introduction to the claims reserving methodology applied in the general insurance with the focus on the agragated data represented in the form of triangle schemes. First the basic deterministic methods are to be presented including the Chain ladder method as the most known and widely used tool in claims reserving. Next we will concentrate on the stochastic approaches. The method of bootstrapping is to be described more in detail as it is the main topic of this thesis. Finally the accuracy of the prediction of several specific models and algorithms is to be examined with the goal of their overall comparison (using randomly generated input data).
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