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Optimal Risk Classification with an Application to Substandard Annuities

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  • Nadine Gatzert
  • Gudrun Schmitt-Hoermann
  • Hato Schmeiser

Abstract

Substandard annuities pay higher pensions to individuals with impaired health and thus require special underwriting of applicants. Although such risk classification can substantially increase a company's profitability, these products are uncommon except for the well-established U.K. market. In this paper we comprehensively analyze this issue and make several contributions to the literature. First, we describe enhanced, impaired life, and care annuities, and then we discuss the underwriting process and underwriting risk related thereto. Second, we propose a theoretical model to determine the optimal profit-maximizing risk classification system for substandard annuities. Based on the model framework and for given price-demand dependencies, we formally show the effect of classification costs and costs of underwriting risk on profitability for insurers. Risk classes are distinguished by the average mortality of contained insureds, whereby mortality heterogeneity is included by means of a frailty model. Third, we discuss key aspects regarding a practical implementation of our model as well as possible market entry barriers for substandard annuity providers.

Suggested Citation

  • Nadine Gatzert & Gudrun Schmitt-Hoermann & Hato Schmeiser, 2012. "Optimal Risk Classification with an Application to Substandard Annuities," North American Actuarial Journal, Taylor & Francis Journals, vol. 16(4), pages 462-486.
    • Handle: RePEc:taf:uaajxx:v:16:y:2012:i:4:p:462-486
    DOI: 10.1080/10920277.2012.10597643
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    Cited by:

    1. Chen, An & Fuino, Michel & Sehner, Thorsten & Wagner, Joël, 2022. "Valuation of long-term care options embedded in life annuities," Annals of Actuarial Science, Cambridge University Press, vol. 16(1), pages 68-94, March.
    2. Martin Eling & Irina Gemmo & Danjela Guxha & Hato Schmeiser, 2024. "Big data, risk classification, and privacy in insurance markets," The Geneva Risk and Insurance Review, Palgrave Macmillan;International Association for the Study of Insurance Economics (The Geneva Association), vol. 49(1), pages 75-126, March.
    3. Ermanno Pitacco & Daniela Y. Tabakova, 2022. "Special-Rate Life Annuities: Analysis of Portfolio Risk Profiles," Risks, MDPI, vol. 10(3), pages 1-22, March.
    4. Mao Hong & Carson James M. & Ostaszewski Krzysztof M., 2018. "Optimal Price Setting and Insurer Capital Management in a Multiple Line Context," Asia-Pacific Journal of Risk and Insurance, De Gruyter, vol. 12(1), pages 1-22, January.

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