scholarly journals Recursive Credibility Formula for Chain Ladder Factors and the Claims Development Result

2009 ◽  
Vol 39 (1) ◽  
pp. 275-306 ◽  
Author(s):  
Hans Bühlmann ◽  
Massimo De Felice ◽  
Alois Gisler ◽  
Franco Moriconi ◽  
Mario V. Wüthrich
Keyword(s):  
Life Insurance ◽  
Solvency Ii ◽  
Mean Square ◽  
Conditional Mean ◽  
Loss Reserving ◽  
Chain Ladder ◽  
One Year ◽  
The One ◽  
Development Result ◽  
Recursive Representation

AbstractIn recent Solvency II considerations much effort has been put into the development of appropriate models for the study of the one-year loss reserving uncertainty in non-life insurance. In this article we derive formulas for the conditional mean square error of prediction of the one-year claims development result in the context of the Bayes chain ladder model studied in Gisler-Wüthrich. The key to these formulas is a recursive representation for the results obtained in Gisler-Wüthrich.

scholarly journals A Bayesian Internal Model for Reserve Risk: An Extension of the Correlated Chain Ladder

Risks ◽  
2020 ◽  
Vol 8 (4) ◽  
pp. 125
Author(s):  
Carnevale Giulio Ercole ◽  
Clemente Gian Paolo
Keyword(s):  
Internal Model ◽  
Predictive Distribution ◽  
Solvency Ii ◽  
Risk Profile ◽  
Formula One ◽  
Life Insurer ◽  
Chain Ladder ◽  
One Year ◽  
The One ◽  
Traditional Approaches

The goal of this paper was to exploit the Bayesian approach and MCMC procedures to structure an internal model to quantify the reserve risk of a non-life insurer under Solvency II regulation. To this aim, we provide an extension of the Correlated Chain Ladder (CCL) model to the one-year time horizon. In this way, we obtain the predictive distribution of the next year obligations and we are able to assess a capital requirement compliant with Solvency II framework. Numerical results compare the one-year CCL with other traditional approaches, such as Re-Reserving and the Merz and Wüthrich formula. One-year CCL proves to be a legitimate alternative, providing values comparable with the more traditional approaches and more robust and accurate risk estimations, that embed external knowledge not present in the data and allow for a more precise and tailored representation of the risk profile of the insurer.

scholarly journals Prediction uncertainties in the Cape Cod reserving method

2015 ◽  
Vol 9 (2) ◽  
pp. 239-263 ◽  
Author(s):  
Annina Saluz
Keyword(s):  
Stochastic Model ◽  
Mean Square Error ◽  
Cape Cod ◽  
Parameter Estimates ◽  
Mean Square ◽  
Established Method ◽  
Distribution Free ◽  
Conditional Mean ◽  
Chain Ladder ◽  
Development Result

AbstractThe Cape Cod (CC) method was designed by Bühlmann and Straub in order to overcome some shortcomings of the chain ladder (CL) method. Owing to its simplicity and because of the advantages over the CL method, the CC method has become a well-established method in practice. In this paper we consider a distribution-free stochastic model for the CC method. Within this model we give the parameter estimates and we derive estimates for the conditional mean square error of prediction for the CC method. In addition, we derive an estimate for the uncertainty in the claims development result.

scholarly journals AN INDUSTRY QUESTION: THE ULTIMATE AND ONE-YEAR RESERVING UNCERTAINTY FOR DIFFERENT NON-LIFE RESERVING METHODOLOGIES

2014 ◽  
Vol 44 (3) ◽  
pp. 495-499 ◽  
Author(s):  
Eric Dal Moro ◽  
Joseph Lo
Keyword(s):  
Closed Form ◽  
Internal Models ◽  
Cape Cod ◽  
Best Estimate ◽  
To Come ◽  
Chain Ladder ◽  
One Year ◽  
The One ◽  
Best Estimates

AbstractIn the industry, generally, reserving actuaries use a mix of reserving methods to derive their best estimates. On the basis of the best estimate, Solvency 2 requires the use of a one-year volatility of the reserves. When internal models are used, such one-year volatility has to be provided by the reserving actuaries. Due to the lack of closed-form formulas for the one-year volatility of Bornhuetter-Ferguson, Cape-Cod and Benktander-Hovinen, reserving actuaries have limited possibilities to estimate such volatility apart from scaling from tractable models, which are based on other reserving methods. However, such scaling is technically difficult to justify cleanly and awkward to interact with. The challenge described in this editorial is therefore to come up with similar models like those of Mack or Merz-Wüthrich for the chain ladder, but applicable to Bornhuetter-Ferguson, mix Chain-Ladder and Bornhuetter-Ferguson, potentially Cape-Cod and Benktander-Hovinen — and their mixtures.

scholarly journals MODELING THE MORTALITY TREND UNDER MODERN SOLVENCY REGIMES

2013 ◽  
Vol 44 (1) ◽  
pp. 1-38 ◽  
Author(s):  
Matthias Börger ◽  
Daniel Fleischer ◽  
Nikita Kuksin
Keyword(s):  
Solvency Ii ◽  
Capital Requirements ◽  
Longevity Risk ◽  
Mortality Trend ◽  
Swiss Solvency Test ◽  
Solvency Capital ◽  
Simultaneous Modeling ◽  
One Year ◽  
The One ◽  
Solvency Regimes

AbstractStochastic modeling of mortality/longevity risks is necessary for internal models of (re)insurers under the new solvency regimes, such as Solvency II and the Swiss Solvency Test. In this paper, we propose a mortality model which fulfills all requirements imposed by these regimes. We show how the model can be calibrated and applied to the simultaneous modeling of both mortality and longevity risk for several populations. The main contribution of this paper is a stochastic trend component which explicitly models changes in the long-term mortality trend assumption over time. This allows to quantify mortality and longevity risk over the one-year time horizon prescribed by the solvency regimes without relying on nested simulations. We illustrate the practical ability of our model by calculating solvency capital requirements for some example portfolios, and we compare these capital requirements with those from the Solvency II standard formula.

scholarly journals Mean Square Error of Prediction in the Bornhuetter–Ferguson Claims Reserving Method

2009 ◽  
Vol 4 (1) ◽  
pp. 7-31 ◽  
Author(s):  
D. H. Alai ◽  
M. Merz ◽  
M. V. Wüthrich
Keyword(s):  
Mean Square Error ◽  
Generalized Linear Models ◽  
Linear Models ◽  
Poisson Model ◽  
Development Pattern ◽  
Mean Square ◽  
Conditional Mean ◽  
Major Subject ◽  
Chain Ladder

ABSTRACTThe prediction of adequate claims reserves is a major subject in actuarial practice and science. Due to their simplicity, the chain ladder (CL) and Bornhuetter–Ferguson (BF) methods are the most commonly used claims reserving methods in practice. However, in contrast to the CL method, no estimator for the conditional mean square error of prediction (MSEP) of the ultimate claim has been derived in the BF method until now, and as such, this paper aims to fill that gap. This will be done in the framework of generalized linear models (GLM) using the (overdispersed) Poisson model motivation for the use of CL factor estimates in the estimation of the claims development pattern.

scholarly journals The Prediction Error of the Chain Ladder Method (With Application to Real Data)

2020 ◽  
Vol 12 (12) ◽  
pp. 14
Author(s):  
Afaf Antar Zohry ◽  
Mostafa Abdelghany Ahmed
Keyword(s):  
Prediction Error ◽  
Real Data ◽  
Solvency Ii ◽  
Insurance Companies ◽  
Mean Square ◽  
Recursive Model ◽  
Chain Ladder Method ◽  
The Mean ◽  
Chain Ladder ◽  
S Model

The chain ladder method is the most widely used method of estimating claims reserves due to its simplicity and ease of application. It is very important to know the accuracy of the resulting estimates. Murphy presented a recursive model to estimate the standard error of claims reserves estimates, in line with the solvency ii requirements as a new regulatory framework adjusted according to risk, which requires the necessity to estimate the error and uncertainty of the claims reserving estimates. In Murphy's model, the mean square error (MSE) is analyzed into its components: variance and bias. In this paper, the recursive model of Murphy was used to estimate the prediction error in claims reserves estimates of General Accident & Miscellaneous Insurance in one of the Egyptian insurance companies.

scholarly journals Advantages and disadvantages of loss reserving methods in non-life insurance

2019 ◽  
Vol 29 (4) ◽  
pp. 553-561
Author(s):  
Jelena Kocovic ◽  
Mirela Mitrasevic ◽  
Dejan Trifunovic
Keyword(s):  
Comparative Analysis ◽  
Life Insurance ◽  
Ratio Method ◽  
Practical Case ◽  
Loss Ratio ◽  
Advantages And Disadvantages ◽  
Chain Ladder Method ◽  
Loss Reserving ◽  
Chain Ladder

We analyse characteristics of the three most commonly used methods for estimating loss reserves in non life insurance: the chain ladder method, the loss ratio method, and the Bornhuetter-Ferguson method. Our aim is to give a comparative analysis of the results obtained from applying these methods to a practical case, and to put emphasis on their advantages and disadvantages.

scholarly journals Investment Activities of Polish Insurance Companies Before and After Solvency II

2021 ◽  
Vol 13 (1) ◽  
pp. 229-242
Author(s):  
Daniel Szaniewski
Keyword(s):  
Life Insurance ◽  
New Technologies ◽  
Distribution Channels ◽  
Solvency Ii ◽  
Insurance Companies ◽  
Legal Regulations ◽  
Legal Basis ◽  
Domestic Life ◽  
Before And After ◽  
The One

Abstract Insurance companies operate in a turbulent, constantly changing environment. The insurance market plays an important role in the economy. On the one hand, it is characterized by the dynamic development of services based on new technologies and distribution channels, and on the other hand, it is subject to transformations related to changes in the scope of conducting insurance activities – including new legal regulations – and has to counter global challenges, such as the crisis which started in 2007 on the American financial market. In such realities, insurers must manage their investment activities. The article indicates the legal basis of the restrictions applicable to insurance companies in relation to their investment activities. The Solvency II system is discussed and the most important differences from its predecessor – Solvency I – are presented, and there is an analysis of the structure of investments of domestic life and non-life insurance companies.

THE RESERVE UNCERTAINTIES IN THE CHAIN LADDER MODEL OF MACK REVISITED

2019 ◽  
Vol 49 (03) ◽  
pp. 787-821
Author(s):  
Alois Gisler
Keyword(s):  
Taylor Expansion ◽  
Distribution Free ◽  
First Order ◽  
Ladder Model ◽  
Run Off ◽  
Full Picture ◽  
Chain Ladder ◽  
One Year ◽  
The One

AbstractWe revisit the “full picture” of the claims development uncertainty in Mack’s (1993) distribution-free stochastic chain ladder model. We derive the uncertainty estimators in a new and easily understandable way, which is much simpler than the derivation found so far in the literature, and compare them with the well known estimators of Mack and of Merz–Wüthrich.Our uncertainty estimators of the one-year run-off risks are new and different to the Merz–Wüthrich formulas. But if we approximate our estimators by a first order Taylor expansion, we obtain equivalent but simpler formulas. As regards the ultimate run-off risk, we obtain the same formulas as Mack for single accident years and an equivalent but better interpretable formula for the total over all accident years.

The one-year non-life insurance risk

2009 ◽  
Vol 45 (2) ◽  
pp. 203-208 ◽  
Author(s):  
Esbjörn Ohlsson ◽  
Jan Lauzeningks
Keyword(s):  
Life Insurance ◽  
Insurance Risk ◽  
One Year ◽  
The One
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