Quantifying Portfolio Demutualization: A Benchmark-Relative Pooling--Profiling Scale
Abstract
Insurance pricing combines pooling with differentiation: a tariff may leave benchmark differences in expected loss partly mutualized or translate them into policy-level premium differences. We propose a benchmark-relative pooling--profiling scale with two complementary coordinates. The coupled Lp coordinate measures policy-level alignment between an evaluated tariff and a stated benchmark pure premium, whereas the marginal Wasserstein coordinate compares their exposure-weighted premium distributions. The difference between their residual p-costs defines an allocation mismatch. Under portfolio balance, the coupled L1 coordinate has an exact actuarial interpretation: it is the fraction of the transfer volume induced by full pooling that the tariff removes. Synthetic and motor-insurance applications show that broad classes, proxies, shrinkage and tail caps can affect marginal differentiation, policy-level allocation and transfers differently. A barycentric group-parity intervention further shows that conditional premium disparities can fall mainly through reallocation and restored benchmark-relative transfers, with little change in marginal differentiation.
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BibTeX
@misc{charpentier2026quantifying,
title = {{Quantifying Portfolio Demutualization: A Benchmark-Relative Pooling--Profiling Scale}},
author = {Arthur Charpentier and Laurence Barry},
howpublished = {arXiv},
year = {2026},
month = sep,
doi = {10.48550/arxiv.2609.23294},
eprint = {2609.23294},
archivePrefix = {arXiv},
url = {https://arxiv.org/abs/2609.23294},
note = {CC BY-NC-ND 4.0},
}
RIS
TY - UNPB
TI - Quantifying Portfolio Demutualization: A Benchmark-Relative Pooling--Profiling Scale
AU - Arthur Charpentier
AU - Laurence Barry
PY - 2026
DA - 2026/09/20
PB - arXiv
DO - 10.48550/arxiv.2609.23294
UR - https://arxiv.org/abs/2609.23294
AB - Insurance pricing combines pooling with differentiation: a tariff may leave benchmark differences in expected loss partly mutualized or translate them into policy-level premium differences. We propose a benchmark-relative pooling--profiling scale with two complementary coordinates. The coupled L^p coordinate measures policy-level alignment between an evaluated tariff and a stated benchmark pure premium, whereas the marginal Wasserstein coordinate compares their exposure-weighted premium distributions. The difference between their residual p-costs defines an allocation mismatch. Under portfolio balance, the coupled L^1 coordinate has an exact actuarial interpretation: it is the fraction of the transfer volume induced by full pooling that the tariff removes. Synthetic and motor-insurance applications show that broad classes, proxies, shrinkage and tail caps can affect marginal differentiation, policy-level allocation and transfers differently. A barycentric group-parity intervention further shows that conditional premium disparities can fall mainly through reallocation and restored benchmark-relative transfers, with little change in marginal differentiation.
ER -