Credibility Distribution Estimation with Weighted or Grouped Observations
In non-life insurance practice, actuaries are often faced with the challenge of predicting the number of claims and claim amounts to be incurred at any given time, which serve to implement fair pricing and reserves given the nature of the risk. This paper extends Jewell’s credible distribution in te...
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| Format: | Article |
| Language: | English |
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MDPI AG
2024-01-01
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| Series: | Risks |
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| Online Access: | https://www.mdpi.com/2227-9091/12/1/10 |
| _version_ | 1797342589854154752 |
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| author | Georgios Pitselis |
| author_facet | Georgios Pitselis |
| author_sort | Georgios Pitselis |
| collection | DOAJ |
| description | In non-life insurance practice, actuaries are often faced with the challenge of predicting the number of claims and claim amounts to be incurred at any given time, which serve to implement fair pricing and reserves given the nature of the risk. This paper extends Jewell’s credible distribution in terms of forecasting the distribution of individual risk in cases where the observations are weighted or are grouped in intervals. More specifically, we show how empirical distribution functions can be embedded within Bühlmann’s and Straub’s credibility model. The optimal projection theorem is applied for credibility estimation and more insight into the derivation of the credibility distribution estimators is also provided. In addition, distribution credibility estimators are established and numerical illustrations are presented herein. Two examples of distribution credibility estimation are given, one with insurance loss data and the other with industry financial data. |
| first_indexed | 2024-03-08T10:35:28Z |
| format | Article |
| id | doaj.art-74733b19765f450093039bef8e9fe717 |
| institution | Directory Open Access Journal |
| issn | 2227-9091 |
| language | English |
| last_indexed | 2024-03-08T10:35:28Z |
| publishDate | 2024-01-01 |
| publisher | MDPI AG |
| record_format | Article |
| series | Risks |
| spelling | doaj.art-74733b19765f450093039bef8e9fe7172024-01-26T18:21:02ZengMDPI AGRisks2227-90912024-01-011211010.3390/risks12010010Credibility Distribution Estimation with Weighted or Grouped ObservationsGeorgios Pitselis0Department of Statistics & Insurance Science, University of Piraeus, 80 Karaoli & Dimitriou Str. T. K., 18534 Piraeus, GreeceIn non-life insurance practice, actuaries are often faced with the challenge of predicting the number of claims and claim amounts to be incurred at any given time, which serve to implement fair pricing and reserves given the nature of the risk. This paper extends Jewell’s credible distribution in terms of forecasting the distribution of individual risk in cases where the observations are weighted or are grouped in intervals. More specifically, we show how empirical distribution functions can be embedded within Bühlmann’s and Straub’s credibility model. The optimal projection theorem is applied for credibility estimation and more insight into the derivation of the credibility distribution estimators is also provided. In addition, distribution credibility estimators are established and numerical illustrations are presented herein. Two examples of distribution credibility estimation are given, one with insurance loss data and the other with industry financial data.https://www.mdpi.com/2227-9091/12/1/10credibility distribution estimationempirical Bayes |
| spellingShingle | Georgios Pitselis Credibility Distribution Estimation with Weighted or Grouped Observations Risks credibility distribution estimation empirical Bayes |
| title | Credibility Distribution Estimation with Weighted or Grouped Observations |
| title_full | Credibility Distribution Estimation with Weighted or Grouped Observations |
| title_fullStr | Credibility Distribution Estimation with Weighted or Grouped Observations |
| title_full_unstemmed | Credibility Distribution Estimation with Weighted or Grouped Observations |
| title_short | Credibility Distribution Estimation with Weighted or Grouped Observations |
| title_sort | credibility distribution estimation with weighted or grouped observations |
| topic | credibility distribution estimation empirical Bayes |
| url | https://www.mdpi.com/2227-9091/12/1/10 |
| work_keys_str_mv | AT georgiospitselis credibilitydistributionestimationwithweightedorgroupedobservations |