Model error (or ambiguity) and its estimation, with particular application to loss reserving
This paper is concerned with the estimation of forecast error, particularly in relation to insurance loss reserving. Forecast error is generally regarded as consisting of three components, namely parameter, process and model errors. The first two of these components, and their estimation, are well u...
Ausführliche Beschreibung
Gespeichert in:
| Autor*in: |
Taylor, Greg [verfasserIn] Mc Guire, Gráinne [verfasserIn] |
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| Format: |
E-Artikel |
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| Sprache: |
Englisch |
| Erschienen: |
2023 |
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| Rechteinformationen: |
Open Access Namensnennung 4.0 International ; CC BY 4.0 |
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| Schlagwörter: |
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| Übergeordnetes Werk: |
Enthalten in: Risks - Basel : MDPI, 2013, 11(2023), 11 vom: Nov., Artikel-ID 185, Seite 1-28 |
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| Übergeordnetes Werk: |
volume:11 ; year:2023 ; number:11 ; month:11 ; elocationid:185 ; pages:1-28 |
| Links: |
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| DOI / URN: |
10.3390/risks11110185 |
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| Katalog-ID: |
1872235727 |
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| 520 | |a This paper is concerned with the estimation of forecast error, particularly in relation to insurance loss reserving. Forecast error is generally regarded as consisting of three components, namely parameter, process and model errors. The first two of these components, and their estimation, are well understood, but less so model error. Model error itself is considered in two parts: one part that is capable of estimation from past data (internal model error), and another part that is not (external model error). Attention is focused here on internal model error. Estimation of this error component is approached by means of Bayesian model averaging, using the Bayesian interpretation of the LASSO. This is used to generate a set of admissible models, each with its prior probability and likelihood of observed data. A posterior on the model set, conditional on the data, may then be calculated. An estimate of model error (for a loss reserve estimate) is obtained as the variance of the loss reserve according to this posterior. The population of models entering materially into the support of the posterior may turn out to be "thinner" than desired, and bootstrapping of the LASSO is used to increase this population. This also provides the bonus of an estimate of parameter error. It turns out that the estimates of parameter and model errors are entangled, and dissociation of them is at least difficult, and possibly not even meaningful. These matters are discussed. The majority of the discussion applies to forecasting generally, but numerical illustration of the concepts is given in relation to insurance data and the problem of insurance loss reserving. | ||
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10.3390/risks11110185 doi (DE-627)1872235727 (DE-599)KXP1872235727 DE-627 ger DE-627 rda eng Taylor, Greg verfasserin (DE-588)1209505673 (DE-627)1697033245 aut Model error (or ambiguity) and its estimation, with particular application to loss reserving Greg Taylor and Gráinne McGuire 2023 Text txt rdacontent Computermedien c rdamedia Online-Ressource cr rdacarrier DE-206 Open Access Controlled Vocabulary for Access Rights http://purl.org/coar/access_right/c_abf2 This paper is concerned with the estimation of forecast error, particularly in relation to insurance loss reserving. Forecast error is generally regarded as consisting of three components, namely parameter, process and model errors. The first two of these components, and their estimation, are well understood, but less so model error. Model error itself is considered in two parts: one part that is capable of estimation from past data (internal model error), and another part that is not (external model error). Attention is focused here on internal model error. Estimation of this error component is approached by means of Bayesian model averaging, using the Bayesian interpretation of the LASSO. This is used to generate a set of admissible models, each with its prior probability and likelihood of observed data. A posterior on the model set, conditional on the data, may then be calculated. An estimate of model error (for a loss reserve estimate) is obtained as the variance of the loss reserve according to this posterior. The population of models entering materially into the support of the posterior may turn out to be "thinner" than desired, and bootstrapping of the LASSO is used to increase this population. This also provides the bonus of an estimate of parameter error. It turns out that the estimates of parameter and model errors are entangled, and dissociation of them is at least difficult, and possibly not even meaningful. These matters are discussed. The majority of the discussion applies to forecasting generally, but numerical illustration of the concepts is given in relation to insurance data and the problem of insurance loss reserving. DE-206 Namensnennung 4.0 International CC BY 4.0 cc https://creativecommons.org/licenses/by/4.0/ Bayesian model averaging (dpeaa)DE-206 bootstrap (dpeaa)DE-206 bootstrap matrix (dpeaa)DE-206 forecast error (dpeaa)DE-206 GLM (dpeaa)DE-206 internal model structure error (dpeaa)DE-206 LASSO (dpeaa)DE-206 loss reserving (dpeaa)DE-206 model ambiguity (dpeaa)DE-206 model error (dpeaa)DE-206 model uncertainty (dpeaa)DE-206 Mc Guire, Gráinne verfasserin (DE-588)171907043 (DE-627)370493664 (DE-576)132661101 aut Enthalten in Risks Basel : MDPI, 2013 11(2023), 11 vom: Nov., Artikel-ID 185, Seite 1-28 Online-Ressource (DE-627)737288485 (DE-600)2704357-5 (DE-576)379467852 2227-9091 nnns volume:11 year:2023 number:11 month:11 elocationid:185 pages:1-28 https://www.mdpi.com/2227-9091/11/11/185/pdf?version=1698236005 Verlag kostenfrei https://doi.org/10.3390/risks11110185 Resolving-System kostenfrei GBV_USEFLAG_U GBV_ILN_26 ISIL_DE-206 SYSFLAG_1 GBV_KXP GBV_ILN_11 GBV_ILN_20 GBV_ILN_22 GBV_ILN_23 GBV_ILN_24 GBV_ILN_39 GBV_ILN_40 GBV_ILN_60 GBV_ILN_62 GBV_ILN_63 GBV_ILN_65 GBV_ILN_69 GBV_ILN_70 GBV_ILN_73 GBV_ILN_95 GBV_ILN_105 GBV_ILN_110 GBV_ILN_151 GBV_ILN_152 GBV_ILN_161 GBV_ILN_206 GBV_ILN_213 GBV_ILN_230 GBV_ILN_285 GBV_ILN_293 GBV_ILN_370 GBV_ILN_602 GBV_ILN_2009 GBV_ILN_2014 GBV_ILN_2034 GBV_ILN_2055 GBV_ILN_2108 GBV_ILN_2111 GBV_ILN_2129 GBV_ILN_4012 GBV_ILN_4037 GBV_ILN_4046 GBV_ILN_4112 GBV_ILN_4125 GBV_ILN_4126 GBV_ILN_4249 GBV_ILN_4305 GBV_ILN_4306 GBV_ILN_4307 GBV_ILN_4313 GBV_ILN_4322 GBV_ILN_4323 GBV_ILN_4324 GBV_ILN_4325 GBV_ILN_4326 GBV_ILN_4335 GBV_ILN_4338 GBV_ILN_4367 GBV_ILN_4700 GBV_ILN_2403 GBV_ILN_2403 ISIL_DE-LFER AR 11 2023 11 11 185 1-28 26 01 0206 4428046898 x1z 07-12-23 2403 01 DE-LFER 4451687365 00 --%%-- --%%-- n --%%-- l01 09-01-24 2403 01 DE-LFER https://doi.org/10.3390/risks11110185 2403 01 DE-LFER https://www.mdpi.com/2227-9091/11/11/185/pdf?version=1698236005 |
| spelling |
10.3390/risks11110185 doi (DE-627)1872235727 (DE-599)KXP1872235727 DE-627 ger DE-627 rda eng Taylor, Greg verfasserin (DE-588)1209505673 (DE-627)1697033245 aut Model error (or ambiguity) and its estimation, with particular application to loss reserving Greg Taylor and Gráinne McGuire 2023 Text txt rdacontent Computermedien c rdamedia Online-Ressource cr rdacarrier DE-206 Open Access Controlled Vocabulary for Access Rights http://purl.org/coar/access_right/c_abf2 This paper is concerned with the estimation of forecast error, particularly in relation to insurance loss reserving. Forecast error is generally regarded as consisting of three components, namely parameter, process and model errors. The first two of these components, and their estimation, are well understood, but less so model error. Model error itself is considered in two parts: one part that is capable of estimation from past data (internal model error), and another part that is not (external model error). Attention is focused here on internal model error. Estimation of this error component is approached by means of Bayesian model averaging, using the Bayesian interpretation of the LASSO. This is used to generate a set of admissible models, each with its prior probability and likelihood of observed data. A posterior on the model set, conditional on the data, may then be calculated. An estimate of model error (for a loss reserve estimate) is obtained as the variance of the loss reserve according to this posterior. The population of models entering materially into the support of the posterior may turn out to be "thinner" than desired, and bootstrapping of the LASSO is used to increase this population. This also provides the bonus of an estimate of parameter error. It turns out that the estimates of parameter and model errors are entangled, and dissociation of them is at least difficult, and possibly not even meaningful. These matters are discussed. The majority of the discussion applies to forecasting generally, but numerical illustration of the concepts is given in relation to insurance data and the problem of insurance loss reserving. DE-206 Namensnennung 4.0 International CC BY 4.0 cc https://creativecommons.org/licenses/by/4.0/ Bayesian model averaging (dpeaa)DE-206 bootstrap (dpeaa)DE-206 bootstrap matrix (dpeaa)DE-206 forecast error (dpeaa)DE-206 GLM (dpeaa)DE-206 internal model structure error (dpeaa)DE-206 LASSO (dpeaa)DE-206 loss reserving (dpeaa)DE-206 model ambiguity (dpeaa)DE-206 model error (dpeaa)DE-206 model uncertainty (dpeaa)DE-206 Mc Guire, Gráinne verfasserin (DE-588)171907043 (DE-627)370493664 (DE-576)132661101 aut Enthalten in Risks Basel : MDPI, 2013 11(2023), 11 vom: Nov., Artikel-ID 185, Seite 1-28 Online-Ressource (DE-627)737288485 (DE-600)2704357-5 (DE-576)379467852 2227-9091 nnns volume:11 year:2023 number:11 month:11 elocationid:185 pages:1-28 https://www.mdpi.com/2227-9091/11/11/185/pdf?version=1698236005 Verlag kostenfrei https://doi.org/10.3390/risks11110185 Resolving-System kostenfrei GBV_USEFLAG_U GBV_ILN_26 ISIL_DE-206 SYSFLAG_1 GBV_KXP GBV_ILN_11 GBV_ILN_20 GBV_ILN_22 GBV_ILN_23 GBV_ILN_24 GBV_ILN_39 GBV_ILN_40 GBV_ILN_60 GBV_ILN_62 GBV_ILN_63 GBV_ILN_65 GBV_ILN_69 GBV_ILN_70 GBV_ILN_73 GBV_ILN_95 GBV_ILN_105 GBV_ILN_110 GBV_ILN_151 GBV_ILN_152 GBV_ILN_161 GBV_ILN_206 GBV_ILN_213 GBV_ILN_230 GBV_ILN_285 GBV_ILN_293 GBV_ILN_370 GBV_ILN_602 GBV_ILN_2009 GBV_ILN_2014 GBV_ILN_2034 GBV_ILN_2055 GBV_ILN_2108 GBV_ILN_2111 GBV_ILN_2129 GBV_ILN_4012 GBV_ILN_4037 GBV_ILN_4046 GBV_ILN_4112 GBV_ILN_4125 GBV_ILN_4126 GBV_ILN_4249 GBV_ILN_4305 GBV_ILN_4306 GBV_ILN_4307 GBV_ILN_4313 GBV_ILN_4322 GBV_ILN_4323 GBV_ILN_4324 GBV_ILN_4325 GBV_ILN_4326 GBV_ILN_4335 GBV_ILN_4338 GBV_ILN_4367 GBV_ILN_4700 GBV_ILN_2403 GBV_ILN_2403 ISIL_DE-LFER AR 11 2023 11 11 185 1-28 26 01 0206 4428046898 x1z 07-12-23 2403 01 DE-LFER 4451687365 00 --%%-- --%%-- n --%%-- l01 09-01-24 2403 01 DE-LFER https://doi.org/10.3390/risks11110185 2403 01 DE-LFER https://www.mdpi.com/2227-9091/11/11/185/pdf?version=1698236005 |
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10.3390/risks11110185 doi (DE-627)1872235727 (DE-599)KXP1872235727 DE-627 ger DE-627 rda eng Taylor, Greg verfasserin (DE-588)1209505673 (DE-627)1697033245 aut Model error (or ambiguity) and its estimation, with particular application to loss reserving Greg Taylor and Gráinne McGuire 2023 Text txt rdacontent Computermedien c rdamedia Online-Ressource cr rdacarrier DE-206 Open Access Controlled Vocabulary for Access Rights http://purl.org/coar/access_right/c_abf2 This paper is concerned with the estimation of forecast error, particularly in relation to insurance loss reserving. Forecast error is generally regarded as consisting of three components, namely parameter, process and model errors. The first two of these components, and their estimation, are well understood, but less so model error. Model error itself is considered in two parts: one part that is capable of estimation from past data (internal model error), and another part that is not (external model error). Attention is focused here on internal model error. Estimation of this error component is approached by means of Bayesian model averaging, using the Bayesian interpretation of the LASSO. This is used to generate a set of admissible models, each with its prior probability and likelihood of observed data. A posterior on the model set, conditional on the data, may then be calculated. An estimate of model error (for a loss reserve estimate) is obtained as the variance of the loss reserve according to this posterior. The population of models entering materially into the support of the posterior may turn out to be "thinner" than desired, and bootstrapping of the LASSO is used to increase this population. This also provides the bonus of an estimate of parameter error. It turns out that the estimates of parameter and model errors are entangled, and dissociation of them is at least difficult, and possibly not even meaningful. These matters are discussed. The majority of the discussion applies to forecasting generally, but numerical illustration of the concepts is given in relation to insurance data and the problem of insurance loss reserving. DE-206 Namensnennung 4.0 International CC BY 4.0 cc https://creativecommons.org/licenses/by/4.0/ Bayesian model averaging (dpeaa)DE-206 bootstrap (dpeaa)DE-206 bootstrap matrix (dpeaa)DE-206 forecast error (dpeaa)DE-206 GLM (dpeaa)DE-206 internal model structure error (dpeaa)DE-206 LASSO (dpeaa)DE-206 loss reserving (dpeaa)DE-206 model ambiguity (dpeaa)DE-206 model error (dpeaa)DE-206 model uncertainty (dpeaa)DE-206 Mc Guire, Gráinne verfasserin (DE-588)171907043 (DE-627)370493664 (DE-576)132661101 aut Enthalten in Risks Basel : MDPI, 2013 11(2023), 11 vom: Nov., Artikel-ID 185, Seite 1-28 Online-Ressource (DE-627)737288485 (DE-600)2704357-5 (DE-576)379467852 2227-9091 nnns volume:11 year:2023 number:11 month:11 elocationid:185 pages:1-28 https://www.mdpi.com/2227-9091/11/11/185/pdf?version=1698236005 Verlag kostenfrei https://doi.org/10.3390/risks11110185 Resolving-System kostenfrei GBV_USEFLAG_U GBV_ILN_26 ISIL_DE-206 SYSFLAG_1 GBV_KXP GBV_ILN_11 GBV_ILN_20 GBV_ILN_22 GBV_ILN_23 GBV_ILN_24 GBV_ILN_39 GBV_ILN_40 GBV_ILN_60 GBV_ILN_62 GBV_ILN_63 GBV_ILN_65 GBV_ILN_69 GBV_ILN_70 GBV_ILN_73 GBV_ILN_95 GBV_ILN_105 GBV_ILN_110 GBV_ILN_151 GBV_ILN_152 GBV_ILN_161 GBV_ILN_206 GBV_ILN_213 GBV_ILN_230 GBV_ILN_285 GBV_ILN_293 GBV_ILN_370 GBV_ILN_602 GBV_ILN_2009 GBV_ILN_2014 GBV_ILN_2034 GBV_ILN_2055 GBV_ILN_2108 GBV_ILN_2111 GBV_ILN_2129 GBV_ILN_4012 GBV_ILN_4037 GBV_ILN_4046 GBV_ILN_4112 GBV_ILN_4125 GBV_ILN_4126 GBV_ILN_4249 GBV_ILN_4305 GBV_ILN_4306 GBV_ILN_4307 GBV_ILN_4313 GBV_ILN_4322 GBV_ILN_4323 GBV_ILN_4324 GBV_ILN_4325 GBV_ILN_4326 GBV_ILN_4335 GBV_ILN_4338 GBV_ILN_4367 GBV_ILN_4700 GBV_ILN_2403 GBV_ILN_2403 ISIL_DE-LFER AR 11 2023 11 11 185 1-28 26 01 0206 4428046898 x1z 07-12-23 2403 01 DE-LFER 4451687365 00 --%%-- --%%-- n --%%-- l01 09-01-24 2403 01 DE-LFER https://doi.org/10.3390/risks11110185 2403 01 DE-LFER https://www.mdpi.com/2227-9091/11/11/185/pdf?version=1698236005 |
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10.3390/risks11110185 doi (DE-627)1872235727 (DE-599)KXP1872235727 DE-627 ger DE-627 rda eng Taylor, Greg verfasserin (DE-588)1209505673 (DE-627)1697033245 aut Model error (or ambiguity) and its estimation, with particular application to loss reserving Greg Taylor and Gráinne McGuire 2023 Text txt rdacontent Computermedien c rdamedia Online-Ressource cr rdacarrier DE-206 Open Access Controlled Vocabulary for Access Rights http://purl.org/coar/access_right/c_abf2 This paper is concerned with the estimation of forecast error, particularly in relation to insurance loss reserving. Forecast error is generally regarded as consisting of three components, namely parameter, process and model errors. The first two of these components, and their estimation, are well understood, but less so model error. Model error itself is considered in two parts: one part that is capable of estimation from past data (internal model error), and another part that is not (external model error). Attention is focused here on internal model error. Estimation of this error component is approached by means of Bayesian model averaging, using the Bayesian interpretation of the LASSO. This is used to generate a set of admissible models, each with its prior probability and likelihood of observed data. A posterior on the model set, conditional on the data, may then be calculated. An estimate of model error (for a loss reserve estimate) is obtained as the variance of the loss reserve according to this posterior. The population of models entering materially into the support of the posterior may turn out to be "thinner" than desired, and bootstrapping of the LASSO is used to increase this population. This also provides the bonus of an estimate of parameter error. It turns out that the estimates of parameter and model errors are entangled, and dissociation of them is at least difficult, and possibly not even meaningful. These matters are discussed. The majority of the discussion applies to forecasting generally, but numerical illustration of the concepts is given in relation to insurance data and the problem of insurance loss reserving. DE-206 Namensnennung 4.0 International CC BY 4.0 cc https://creativecommons.org/licenses/by/4.0/ Bayesian model averaging (dpeaa)DE-206 bootstrap (dpeaa)DE-206 bootstrap matrix (dpeaa)DE-206 forecast error (dpeaa)DE-206 GLM (dpeaa)DE-206 internal model structure error (dpeaa)DE-206 LASSO (dpeaa)DE-206 loss reserving (dpeaa)DE-206 model ambiguity (dpeaa)DE-206 model error (dpeaa)DE-206 model uncertainty (dpeaa)DE-206 Mc Guire, Gráinne verfasserin (DE-588)171907043 (DE-627)370493664 (DE-576)132661101 aut Enthalten in Risks Basel : MDPI, 2013 11(2023), 11 vom: Nov., Artikel-ID 185, Seite 1-28 Online-Ressource (DE-627)737288485 (DE-600)2704357-5 (DE-576)379467852 2227-9091 nnns volume:11 year:2023 number:11 month:11 elocationid:185 pages:1-28 https://www.mdpi.com/2227-9091/11/11/185/pdf?version=1698236005 Verlag kostenfrei https://doi.org/10.3390/risks11110185 Resolving-System kostenfrei GBV_USEFLAG_U GBV_ILN_26 ISIL_DE-206 SYSFLAG_1 GBV_KXP GBV_ILN_11 GBV_ILN_20 GBV_ILN_22 GBV_ILN_23 GBV_ILN_24 GBV_ILN_39 GBV_ILN_40 GBV_ILN_60 GBV_ILN_62 GBV_ILN_63 GBV_ILN_65 GBV_ILN_69 GBV_ILN_70 GBV_ILN_73 GBV_ILN_95 GBV_ILN_105 GBV_ILN_110 GBV_ILN_151 GBV_ILN_152 GBV_ILN_161 GBV_ILN_206 GBV_ILN_213 GBV_ILN_230 GBV_ILN_285 GBV_ILN_293 GBV_ILN_370 GBV_ILN_602 GBV_ILN_2009 GBV_ILN_2014 GBV_ILN_2034 GBV_ILN_2055 GBV_ILN_2108 GBV_ILN_2111 GBV_ILN_2129 GBV_ILN_4012 GBV_ILN_4037 GBV_ILN_4046 GBV_ILN_4112 GBV_ILN_4125 GBV_ILN_4126 GBV_ILN_4249 GBV_ILN_4305 GBV_ILN_4306 GBV_ILN_4307 GBV_ILN_4313 GBV_ILN_4322 GBV_ILN_4323 GBV_ILN_4324 GBV_ILN_4325 GBV_ILN_4326 GBV_ILN_4335 GBV_ILN_4338 GBV_ILN_4367 GBV_ILN_4700 GBV_ILN_2403 GBV_ILN_2403 ISIL_DE-LFER AR 11 2023 11 11 185 1-28 26 01 0206 4428046898 x1z 07-12-23 2403 01 DE-LFER 4451687365 00 --%%-- --%%-- n --%%-- l01 09-01-24 2403 01 DE-LFER https://doi.org/10.3390/risks11110185 2403 01 DE-LFER https://www.mdpi.com/2227-9091/11/11/185/pdf?version=1698236005 |
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10.3390/risks11110185 doi (DE-627)1872235727 (DE-599)KXP1872235727 DE-627 ger DE-627 rda eng Taylor, Greg verfasserin (DE-588)1209505673 (DE-627)1697033245 aut Model error (or ambiguity) and its estimation, with particular application to loss reserving Greg Taylor and Gráinne McGuire 2023 Text txt rdacontent Computermedien c rdamedia Online-Ressource cr rdacarrier DE-206 Open Access Controlled Vocabulary for Access Rights http://purl.org/coar/access_right/c_abf2 This paper is concerned with the estimation of forecast error, particularly in relation to insurance loss reserving. Forecast error is generally regarded as consisting of three components, namely parameter, process and model errors. The first two of these components, and their estimation, are well understood, but less so model error. Model error itself is considered in two parts: one part that is capable of estimation from past data (internal model error), and another part that is not (external model error). Attention is focused here on internal model error. Estimation of this error component is approached by means of Bayesian model averaging, using the Bayesian interpretation of the LASSO. This is used to generate a set of admissible models, each with its prior probability and likelihood of observed data. A posterior on the model set, conditional on the data, may then be calculated. An estimate of model error (for a loss reserve estimate) is obtained as the variance of the loss reserve according to this posterior. The population of models entering materially into the support of the posterior may turn out to be "thinner" than desired, and bootstrapping of the LASSO is used to increase this population. This also provides the bonus of an estimate of parameter error. It turns out that the estimates of parameter and model errors are entangled, and dissociation of them is at least difficult, and possibly not even meaningful. These matters are discussed. The majority of the discussion applies to forecasting generally, but numerical illustration of the concepts is given in relation to insurance data and the problem of insurance loss reserving. DE-206 Namensnennung 4.0 International CC BY 4.0 cc https://creativecommons.org/licenses/by/4.0/ Bayesian model averaging (dpeaa)DE-206 bootstrap (dpeaa)DE-206 bootstrap matrix (dpeaa)DE-206 forecast error (dpeaa)DE-206 GLM (dpeaa)DE-206 internal model structure error (dpeaa)DE-206 LASSO (dpeaa)DE-206 loss reserving (dpeaa)DE-206 model ambiguity (dpeaa)DE-206 model error (dpeaa)DE-206 model uncertainty (dpeaa)DE-206 Mc Guire, Gráinne verfasserin (DE-588)171907043 (DE-627)370493664 (DE-576)132661101 aut Enthalten in Risks Basel : MDPI, 2013 11(2023), 11 vom: Nov., Artikel-ID 185, Seite 1-28 Online-Ressource (DE-627)737288485 (DE-600)2704357-5 (DE-576)379467852 2227-9091 nnns volume:11 year:2023 number:11 month:11 elocationid:185 pages:1-28 https://www.mdpi.com/2227-9091/11/11/185/pdf?version=1698236005 Verlag kostenfrei https://doi.org/10.3390/risks11110185 Resolving-System kostenfrei GBV_USEFLAG_U GBV_ILN_26 ISIL_DE-206 SYSFLAG_1 GBV_KXP GBV_ILN_11 GBV_ILN_20 GBV_ILN_22 GBV_ILN_23 GBV_ILN_24 GBV_ILN_39 GBV_ILN_40 GBV_ILN_60 GBV_ILN_62 GBV_ILN_63 GBV_ILN_65 GBV_ILN_69 GBV_ILN_70 GBV_ILN_73 GBV_ILN_95 GBV_ILN_105 GBV_ILN_110 GBV_ILN_151 GBV_ILN_152 GBV_ILN_161 GBV_ILN_206 GBV_ILN_213 GBV_ILN_230 GBV_ILN_285 GBV_ILN_293 GBV_ILN_370 GBV_ILN_602 GBV_ILN_2009 GBV_ILN_2014 GBV_ILN_2034 GBV_ILN_2055 GBV_ILN_2108 GBV_ILN_2111 GBV_ILN_2129 GBV_ILN_4012 GBV_ILN_4037 GBV_ILN_4046 GBV_ILN_4112 GBV_ILN_4125 GBV_ILN_4126 GBV_ILN_4249 GBV_ILN_4305 GBV_ILN_4306 GBV_ILN_4307 GBV_ILN_4313 GBV_ILN_4322 GBV_ILN_4323 GBV_ILN_4324 GBV_ILN_4325 GBV_ILN_4326 GBV_ILN_4335 GBV_ILN_4338 GBV_ILN_4367 GBV_ILN_4700 GBV_ILN_2403 GBV_ILN_2403 ISIL_DE-LFER AR 11 2023 11 11 185 1-28 26 01 0206 4428046898 x1z 07-12-23 2403 01 DE-LFER 4451687365 00 --%%-- --%%-- n --%%-- l01 09-01-24 2403 01 DE-LFER https://doi.org/10.3390/risks11110185 2403 01 DE-LFER https://www.mdpi.com/2227-9091/11/11/185/pdf?version=1698236005 |
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Model error (or ambiguity) and its estimation, with particular application to loss reserving Greg Taylor and Gráinne McGuire Bayesian model averaging (dpeaa)DE-206 bootstrap (dpeaa)DE-206 bootstrap matrix (dpeaa)DE-206 forecast error (dpeaa)DE-206 GLM (dpeaa)DE-206 internal model structure error (dpeaa)DE-206 LASSO (dpeaa)DE-206 loss reserving (dpeaa)DE-206 model ambiguity (dpeaa)DE-206 model error (dpeaa)DE-206 model uncertainty (dpeaa)DE-206 |
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model error (or ambiguity) and its estimation, with particular application to loss reserving |
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Model error (or ambiguity) and its estimation, with particular application to loss reserving |
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This paper is concerned with the estimation of forecast error, particularly in relation to insurance loss reserving. Forecast error is generally regarded as consisting of three components, namely parameter, process and model errors. The first two of these components, and their estimation, are well understood, but less so model error. Model error itself is considered in two parts: one part that is capable of estimation from past data (internal model error), and another part that is not (external model error). Attention is focused here on internal model error. Estimation of this error component is approached by means of Bayesian model averaging, using the Bayesian interpretation of the LASSO. This is used to generate a set of admissible models, each with its prior probability and likelihood of observed data. A posterior on the model set, conditional on the data, may then be calculated. An estimate of model error (for a loss reserve estimate) is obtained as the variance of the loss reserve according to this posterior. The population of models entering materially into the support of the posterior may turn out to be "thinner" than desired, and bootstrapping of the LASSO is used to increase this population. This also provides the bonus of an estimate of parameter error. It turns out that the estimates of parameter and model errors are entangled, and dissociation of them is at least difficult, and possibly not even meaningful. These matters are discussed. The majority of the discussion applies to forecasting generally, but numerical illustration of the concepts is given in relation to insurance data and the problem of insurance loss reserving. |
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This paper is concerned with the estimation of forecast error, particularly in relation to insurance loss reserving. Forecast error is generally regarded as consisting of three components, namely parameter, process and model errors. The first two of these components, and their estimation, are well understood, but less so model error. Model error itself is considered in two parts: one part that is capable of estimation from past data (internal model error), and another part that is not (external model error). Attention is focused here on internal model error. Estimation of this error component is approached by means of Bayesian model averaging, using the Bayesian interpretation of the LASSO. This is used to generate a set of admissible models, each with its prior probability and likelihood of observed data. A posterior on the model set, conditional on the data, may then be calculated. An estimate of model error (for a loss reserve estimate) is obtained as the variance of the loss reserve according to this posterior. The population of models entering materially into the support of the posterior may turn out to be "thinner" than desired, and bootstrapping of the LASSO is used to increase this population. This also provides the bonus of an estimate of parameter error. It turns out that the estimates of parameter and model errors are entangled, and dissociation of them is at least difficult, and possibly not even meaningful. These matters are discussed. The majority of the discussion applies to forecasting generally, but numerical illustration of the concepts is given in relation to insurance data and the problem of insurance loss reserving. |
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This paper is concerned with the estimation of forecast error, particularly in relation to insurance loss reserving. Forecast error is generally regarded as consisting of three components, namely parameter, process and model errors. The first two of these components, and their estimation, are well understood, but less so model error. Model error itself is considered in two parts: one part that is capable of estimation from past data (internal model error), and another part that is not (external model error). Attention is focused here on internal model error. Estimation of this error component is approached by means of Bayesian model averaging, using the Bayesian interpretation of the LASSO. This is used to generate a set of admissible models, each with its prior probability and likelihood of observed data. A posterior on the model set, conditional on the data, may then be calculated. An estimate of model error (for a loss reserve estimate) is obtained as the variance of the loss reserve according to this posterior. The population of models entering materially into the support of the posterior may turn out to be "thinner" than desired, and bootstrapping of the LASSO is used to increase this population. This also provides the bonus of an estimate of parameter error. It turns out that the estimates of parameter and model errors are entangled, and dissociation of them is at least difficult, and possibly not even meaningful. These matters are discussed. The majority of the discussion applies to forecasting generally, but numerical illustration of the concepts is given in relation to insurance data and the problem of insurance loss reserving. |
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| score |
7.4011774 |