Ni, Weihong, Constantinescu, Corina, Reis, Alfredo Egídio dos and Maume-Deschamps, Véronique
(2020)
Pricing foreseeable and unforeseeable risks in insurance portfolios.
[Preprint]
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2008.03123v1.pdf - Submitted version Download (1MB) | Preview |
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.
| Item Type: | Preprint |
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| Additional Information: | arXiv admin note: substantial text overlap with arXiv:1905.07157 |
| Uncontrolled Keywords: | q-fin.GN, q-fin.GN, q-fin.RM |
| Depositing User: | Symplectic Admin |
| Date Deposited: | 15 Sep 2020 07:35 |
| Last Modified: | 17 Mar 2024 12:51 |
| DOI: | 10.48550/arxiv.2008.03123 |
| Related URLs: | |
| URI: | https://livrepository.liverpool.ac.uk/id/eprint/3101172 |
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