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Pricing foreseeable and unforeseeable risks in insurance portfolios

Author

Listed:
  • Weihong Ni

    (ICJ, PSPM)

  • Corina Constantinescu

    (ICJ, PSPM)

  • Alfredo Eg'idio dos Reis

    (ICJ, PSPM)

  • V'eronique Maume-Deschamps

    (ICJ, PSPM)

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.

Suggested Citation

  • Weihong Ni & Corina Constantinescu & Alfredo Eg'idio dos Reis & V'eronique Maume-Deschamps, 2020. "Pricing foreseeable and unforeseeable risks in insurance portfolios," Papers 2008.03123, arXiv.org.
    • Handle: RePEc:arx:papers:2008.03123
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