Pricing foreseeable and unforeseeable risks in insurance portfolios

Weihong Ni; Corina Constantinescu; Alfredo Egídio dos Reis; Véronique Maume-Deschamps

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arXiv · 2008.03123

Pricing foreseeable and unforeseeable risks in insurance portfolios

Weihong Ni·Corina Constantinescu·Alfredo Egídio dos Reis·Véronique Maume-Deschamps

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Abstract

In this manuscript we propose a method for pricing insurance products that cover not only traditional risks, but also unforeseen ones. By considering the Poisson process parameter to be a mixed random variable, we capture the heterogeneity of foreseeable and unforeseeable risks. To illustrate, we estimate the weights for the two risk streams for a real dataset from a Portuguese insurer. To calculate the premium, we set the frequency and severity as distributions that belong to the linear exponential family. Under a Bayesian setup , we show that when working with a finite mixture of conjugate priors, the premium can be estimated by a mixture of posterior means, with updated parameters, depending on claim histories. We emphasise the riskiness of the unforeseeable trend, by choosing heavy-tailed distributions. After estimating distribution parameters involved using the Expectation-Maximization algorithm, we found that Bayesian premiums derived are more reactive to claim trends than traditional ones.

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BibTeX RIS

Weihong Ni, Corina Constantinescu, Alfredo Egídio dos Reis, Véronique Maume-Deschamps. 2020-07-15. Pricing foreseeable and unforeseeable risks in insurance portfolios. https://arxiv.org/abs/2008.03123

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