Insurers record detailed information related to claims (e.g. the cause of the claim) and policies (e.g. the value of the insured risk) for pricing insurance contracts. However, this information is largely neglected when estimating the reserve for future liabilities originating from past exposures.We present a flexible, yet highly interpretable framework for including these claimand policy-specific covariates in a reserving model. Our framework focuses on three building blocks in the development process of a claim: the time to settlement, the number of payments and the size of each payment. We carefully choose a generalized linear model (GLM) to model each of these stochastic building blocks in discrete time. Since GLMs are applied in the pricing of insurance contracts, our project bridges the gap between pricing and reserving methodology. We propose model selection techniques for GLMs adapted for censored data to select the relevant covariates in these modelsand demonstrate how the selected covariatesdetermine the granularity of our reserving model. At one extreme, including many covariates captures the heterogeneity in the development process of individual claims, while at the other extreme, including no covariatescorresponds to specifying a model for data aggregated in two-dimensional contingency tables, similar to the run-off triangles traditionally used by reservingactuaries. The set of selected covariates then naturally determines the position the actuary should take in between those two extremes .  We illustrate our method with case studies on real life insurance data sets. These case studies provide new insights in the covariates driving the development of claims and demonstrate the accuracy and robustness of the reserving methodology over time.
Traditional non-life reserving models largely neglect the vast amount of information collected over the lifetime of a claim. This information includes covariates describing the policy (e.g. the value of the insured risk) , claim cause (e.g. hail) as well as the detailed claim's history (e.g. settlement, payment, involvement lawyer). We present the hierarchical reserving model as a modular framework for integrating a claim's history and claim-specific covariates into the development process . Hierarchical reserving models decompose the joint likelihood of the development process over time. Moreover, they are tailored to the portfolio at hand by adding a layer to the model for each of the registered events (e.g. settlement, payment). Layers are modelled with classical techniques (e.g. generalized linear models) or machine learning methods (e.g. gradient boosting machines) and using claim-specific covariates . As a result of its flexibility, this framework incorporates many existing reserving models, ranging from aggregate models designed for runoff triangles to individual models using claim-specific covariates. This connection allows us to develop a data-driven strategy for choosing between aggregate and individual reserving; an important decision for reserving practitioners that is largely left unexplored in scientific literature. We illustrate our method with a case study on a real life insurance data set. This case study provides new insights in the covariates driving the development of claims and demonstrates the flexibility and robustness of the hierarchical reserving model over time.
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Insurers record detailed information related to claims (e.g. the cause of the claim) and policies
Traditional non-life reserving models largely neglect the vast amount of information collected over the lifetime of a claim. This information includes covariates describing the policy
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for pricing insurance contracts. However, this information is largely neglected when estimating the reserve for future liabilities originating from past exposures.We present a flexible, yet highly interpretable framework for including these claimand policy-specific covariates in a reserving model. Our framework focuses on three building blocks in
, claim cause (e.g. hail) as well as the detailed claim's history (e.g. settlement, payment, involvement lawyer). We present the hierarchical reserving model as a modular framework for integrating a claim's history and claim-specific covariates into
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of a claim: the time to settlement,
. Hierarchical reserving models decompose the joint likelihood of
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number of payments and the size of each payment. We carefully choose a generalized linear model (GLM) to model each of these stochastic building blocks in discrete time. Since GLMs are applied in the pricing of insurance contracts, our project bridges the gap between pricing and reserving methodology. We propose model selection techniques for GLMs adapted for censored data to select the relevant covariates in these modelsand demonstrate how the selected covariatesdetermine the granularity of our reserving model. At one extreme, including many covariates captures the heterogeneity in the development process of individual claims, while at the other extreme, including no covariatescorresponds to specifying a model for data aggregated in two-dimensional contingency tables, similar to the run-off triangles traditionally used by reservingactuaries. The set of selected covariates then naturally determines the position the actuary should take in between those two extremes
development process over time. Moreover, they are tailored to the portfolio at hand by adding a layer to the model for each of the registered events (e.g. settlement, payment). Layers are modelled with classical techniques (e.g. generalized linear models) or machine learning methods (e.g. gradient boosting machines) and using claim-specific covariates
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As a result of its flexibility, this framework incorporates many existing reserving models, ranging from aggregate models designed for runoff triangles to individual models using claim-specific covariates. This connection allows us to develop a data-driven strategy for choosing between aggregate and individual reserving; an important decision for reserving practitioners that is largely left unexplored in scientific literature.
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case studies on
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sets. These case studies provide
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demonstrate the accuracy
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reserving methodology
hierarchical reserving model