A Quantitative Study of Chain Ladder Based Pricing Approaches for Long-Tail Quota Shares

Riegel, Ulrich

doi:10.1017/asb.2015.2

Cited by 5 publications

(4 citation statements)

References 8 publications

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“…We introduce an extension of the additive model that includes an assumption regarding the covariance structure of the volume estimates v i . Similar models for the uncertainty of volume estimates have been used by Gluck (1997) and Riegel (2015) in different contexts. In addition, this extended additive model includes a lognormal assumption for the incremental claims of (at least) the first development year.…”

Section: Introductionmentioning

confidence: 92%

“…, n} are independent. Gluck (1997) and Riegel (2015) use similar assumptions to model uncertainty of volume estimates. Our Model Assumption 4 implies that v −1 i is an unbiased estimator for v −1 i (see Proposition 2.3) and that…”

Section: Model Assumption 4 the Volume Estimate V N Equals The Modelmentioning

confidence: 99%

“…Similar to ε ext , it is possible to use external estimators (or lower and/or upper bounds) for the parameters s 2 k . For instance, if we assume a compound Poisson distribution for S i,1 , then an external estimator for s 2 1 can be calculated from individual claims data, see Riegel (2015).…”

Section: Potential Modifications To the Algorithmmentioning

confidence: 99%

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A Generalized Loss Ratio Method Dealing With Uncertain Volume Measures

Riegel¹

2018

ASTIN Bull.

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Unlike chain ladder, the loss ratio method requires volume measures. Typically, these volumes are assumed to be known. In practice, however, accurate volume measures are rarely available. We interpret the available volumes as estimators for the true volume measures and analyze the consequences for the loss ratio method. In particular, we calculate the mean squared error of prediction, including uncertainty of volume measures, and derive approximately optimal weights for the observed incremental loss ratios. We then introduce a generalization of the loss ratio method that is tailored to the situation of uncertain volume measures and calculate the prediction uncertainty of this generalized loss ratio method.

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Section: Introductionmentioning

confidence: 92%

Section: Model Assumption 4 the Volume Estimate V N Equals The Modelmentioning

confidence: 99%

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A Generalized Loss Ratio Method Dealing With Uncertain Volume Measures

Riegel¹

2018

ASTIN Bull.

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“…For instance, Kasozi et al (2013) indicated that the QS reinsurance does have a positive impact on the survival of insurance companies as it minimizes their ultimate ruin probabilities. Riegle (2015) used the chain ladder (CL) method to predict price uncertainty under a long-tail QS reinsurance treaty. The impact of reinsurance treaties on the insurer's lifetime has been investigated by Fan et al (2017).…”

Section: Introductionmentioning

confidence: 99%

The effect of reinsurance treaties on the cedent loss reserving

Payandeh Najafabadi,

Atatalab

2023

JM2

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Purpose The usual, simple and computationally expensive recovery payment method for a given reinsurance treaty, besides the total run-off triangle, builds a new run-off triangle, say recovery run-off triangle, for the reinsurer’s contribution and predicts the reinsurer’s contribution to the total loss reserves. This paper, without building a recovery run-off triangle, uses the available prior knowledge about a reinsurance treaty to predict the cedent’s loss reserve under five reinsurance treaties. Design/methodology/approach The authors propose a new solution to the problem of how to consider reserving issues when there is a reinsurance treaty for a portfolio of general insurance policies. Considering this when determining pricing or making capital decisions is very important. Findings In particular, it considers the quota share (QS) treaty, surplus (SPL) treaty, excess-of-loss (XL) treaty, largest claims reinsurance (LCR) treaty and excédent du coût moyen relatif (ECOMOR) treaty. Then, it develops a theoretical foundation for predicting the cedent’s loss reserve and evaluating such prediction using the mean square error of prediction (MSEP). The impact of such reinsurance treaties on the variability of the cedent’s loss reserve has been investigated through a simulation study. Originality/value This paper, without building a recovery run-off triangle, uses the available prior knowledge about a reinsurance treaty to predict the cedent’s loss reserve under five reinsurance treaties. In particular, it considers the QS treaty, SPL treaty, XL treaty, LCR treaty and ECOMOR treaty. Then, it develops a theoretical foundation for predicting the cedent’s loss reserve and evaluating such prediction using the MSEP. The impact of such reinsurance treaties on the variability of the cedent’s loss reserve has been investigated through a simulation study.

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Fackler¹

2022

Eur. Actuar. J.

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A Quantitative Study of Chain Ladder Based Pricing Approaches for Long-Tail Quota Shares

Cited by 5 publications

References 8 publications

A Generalized Loss Ratio Method Dealing With Uncertain Volume Measures

A Generalized Loss Ratio Method Dealing With Uncertain Volume Measures

The effect of reinsurance treaties on the cedent loss reserving

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