Abstract
AbstractInnon-life insurance, the payment history can be predictive of the timing of a settlement for individual claims. Ignoring the association between the payment process and the settlement process could bias the prediction of outstanding payments. To address this issue, we introduce into the literature of micro-level loss reserving a joint modeling framework that incorporates longitudinal payments of a claim into the intensity process of claim settlement. We discuss statistical inference and focus on the prediction aspects of the model. We demonstrate applications of the proposed model in the reserving practice with a detailed empirical analysis using data from a property insurance provider. The prediction results from an out-of-sample validation show that the joint model framework outperforms existing reserving models that ignore the payment–settlement association.
Highlights
A loss reserve represents the insurer’s best estimate of outstanding liabilities for claims that occurred on or before a valuation date
The Reported But Not Settled (RBNS) prediction performance of the joint model is compared to existing reserving models using out–of–sample data, and the results suggest that accounting for the payment–settlement association leads to better prediction
More expensive in terms of severity and take longer to settle, suggesting that the payment process is correlated with the settlement process for individual claims
Summary
A loss reserve represents the insurer’s best estimate of outstanding liabilities for claims that occurred on or before a valuation date. Inaccurate prediction of unpaid claims may lead to under-reserving (inadequate reserves) or over-reserving (excessive reserves), which influences the insurer’s key financial metrics that further feeds into the decision making of management, investors, and regulators (Petroni, 1992).
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