A new expression for the true one-year prediction uncertainty in the chain-ladder model of Mack

2021 ◽  
Author(s):  
Filippo Siegenthaler
Keyword(s):  
Prediction Uncertainty ◽  
Ladder Model ◽  
Chain Ladder ◽  
One Year

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.

scholarly journals One-Year and Ultimate Reserve Risk in Mack Chain Ladder Model

Risks ◽  
2021 ◽  
Vol 9 (9) ◽  
pp. 152
Author(s):  
Marcin Szatkowski ◽  
Łukasz Delong
Keyword(s):  
Simulation Study ◽  
Value At Risk ◽  
Risk Measure ◽  
Estimation Error ◽  
Individual Development ◽  
Emergence Pattern ◽  
Ladder Model ◽  
Chain Ladder ◽  
One Year ◽  
The One

We investigate the relation between one-year reserve risk and ultimate reserve risk in Mack Chain Ladder model in a simulation study. The first goal is to validate the so-called linear emergence pattern formula, which maps the ultimate loss to the one-year loss, in case when we measure the risks with Value-at-Risk. The second goal is to estimate the true emergence pattern of the ultimate loss, i.e., the conditional distribution of the one-year loss given the ultimate loss, from which we can properly derive a risk measure for the one-year horizon from the simulations of ultimate losses. Finally, our third goal is to test if classical actuarial distributions can be used for modelling of the outstanding loss from the ultimate and the one-year perspective. In our simulation study, we investigate several synthetic loss triangles with various duration of the claims development process, volatility, skewness, and distributional assumptions of the individual development factors. We quantify the reserve risks without and with the estimation error of the claims development factors.

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 Identification of the age-period-cohort model and the extended chain-ladder model

Biometrika ◽  
2008 ◽  
Vol 95 (4) ◽  
pp. 979-986 ◽  
Author(s):  
D. Kuang ◽  
B. Nielsen ◽  
J. P. Nielsen
Keyword(s):  
Cohort Model ◽  
Ladder Model ◽  
Extended Chain ◽  
Chain Ladder

scholarly journals Forecasting with the age-period-cohort model and the extended chain-ladder model

Biometrika ◽  
2008 ◽  
Vol 95 (4) ◽  
pp. 987-991 ◽  
Author(s):  
D. Kuang ◽  
B. Nielsen ◽  
J. P. Nielsen
Keyword(s):  
Cohort Model ◽  
Ladder Model ◽  
Extended Chain ◽  
Chain Ladder

scholarly journals Bayesian over-dispersed Poisson model and the Bornhuetter & Ferguson claims reserving method

2012 ◽  
Vol 6 (2) ◽  
pp. 258-283 ◽  
Author(s):  
Peter D. England ◽  
Richard J. Verrall ◽  
Mario V. Wüthrich
Keyword(s):  
Poisson Model ◽  
The Other ◽  
Prior Distributions ◽  
Prediction Uncertainty ◽  
General Insurance ◽  
Other Hand ◽  
Different Types ◽  
Chain Ladder ◽  
The One ◽  
Classical Chain

AbstractWe consider the Bayesian over-dispersed Poisson (ODP) model for claims reserving in general insurance. We choose two different types of prior distributions for the parameters and then study the different Bayesian predictors. This study leads, on the one hand, to the classical chain ladder predictor and, on the other hand, to Bornhuetter & Ferguson predictors. We highlight (either analytically or numerically) how these predictors are obtained and how their prediction uncertainty can be determined.

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