Autocalibration by balance correction in nonlife insurance pricing

Michel Denuit () and Julien Trufin ()
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Michel Denuit: Université catholique de Louvain, LIDAM/ISBA, Belgium
Julien Trufin: ULB

No 2022041, LIDAM Discussion Papers ISBA from Université catholique de Louvain, Institute of Statistics, Biostatistics and Actuarial Sciences (ISBA)

Abstract: By exploiting massive amounts of data, machine learning techniques provide actuaries with predictors exhibiting high correlation with claim frequencies and severities. However, these predictors generally fail to achieve financial equilibrium and thus do not qualify as pure premiums. Autocalibration effectively addresses this issue since it ensures that every group of policyholders paying the same premium is on average self-financing, as demonstrated by Denuit et al. (2021), Ciatto et al. (2022), Lindholm et al. (2022) and Wüthrich (2022). These authors proposed balance correction as a way to make any candidate premium autocalibrated. The present paper further studies the effect of balance correction on resulting pure premiums. It is shown that this method is also beneficial in terms of out-of-sample, or predictive Tweedie deviance, Bregman divergence as well as concentration curves. The paper then derives conditions ensuring that the initial predictor and its balance-corrected version are ordered in Lorenz order. Finally, criteria are proposed to rank the balance-corrected versions of two competing predictors in the convex order.

Keywords: Tweedie deviance; Bregman divergence; financial equilibrium; convex order; Lorenz order (search for similar items in EconPapers)
Pages: 17
Date: 2022-12-15
New Economics Papers: this item is included in nep-big and nep-rmg
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