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Optimal rate classification for enhanced annuities

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Zeitschrift für die gesamte Versicherungswissenschaft

Abstract

For a given premium, enhanced annuities pay higher pensions to policyholders with impaired health. Even though risk classification is a common concept in the insurance sector and should allow insurers to increase their profitability, enhanced annuities are rarely offered outside of the United Kingdom. The paper provides a general method of determining an optimal risk classification system for enhanced annuities that will maximize an insurance company’s profits. The cost of risk classification, as well as that incurred when insureds are assigned to inappropriate risk classes (a chief component of underwriting risk), are explicitly considered.

Zusammenfassung

„Enhanced-Annuity“-Versicherungsverträge zahlen ceteris paribus höhere Renten an Versicherungsnehmer mit reduzierter Lebenserwartung. Obwohl Risikoklassifikation (hier: in Abhängigkeit der Lebenserwartung der Versicherten) im Versicherungssektor eine überaus übliche Vorgehensweise ist und grundsätzlich dazu führt, die Profitabilität des Versicherungsunternehmens zu steigern, finden sich „Enhanced-Annuity“-Kontrakte ausserhalb von Grossbritannien nur sehr selten. Die vorliegende Arbeit leitet ein Risikoklassifikationssystem für „Enhanced-Annuity“-Verträge für ein Unternehmen ab, das den erwarteten Gewinn maximieren möchte. Dabei finden sowohl Risikoklassifikationskosten als auch Kosten von Fehlklassifikationen Berücksichtigung.

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Notes

  1. See LIMRA and Ernst and Young (2006, p. 10). Enhanced annuities, impaired life, and care annuities are all subsumed within what are known as “substandard annuities” (for a detailed description, see Gatzert et al. 2008). In the U.K. market, all types of substandard annuities are sometimes referred to as enhanced annuities.

  2. See LIMRA and Ernst and Young (2006, p. 18).

  3. For a detailed explanation, see Doherty (1981).

  4. According to Actuarial Standard of Practice No. 12, a risk classification system is a “system used to assign risks to groups based upon the expected cost or benefit of the coverage or services provided” (Actuarial Standards Board 2005).

  5. The model of mortality heterogeneity in the general population is based on Hoermann and Russ (2008).

  6. See, e.g., Jones (1998, pp. 80–83), Pitacco (2004, p. 15), and Vaupel et al. (1979, p. 440).

  7. See Gatzert et al. (2008).

  8. See Cummins et al. (1983, pp. 83–92).

  9. See, e.g., Pindyck and Rubinfeld (2008, pp. 393–403) and Baumol (1977, pp. 405–406).

  10. For a formal description of this setting, see Gatzert et al. (2008).

  11. See Doherty (1981).

  12. See, e.g., Baumol (1977, pp. 416–417), assuming that the functions are differentiable.

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Authors and Affiliations

  1. Lehrstuhl für Versicherungswirtschaft, Universität Erlangen-Nürnberg, Lange Gasse 20, 90403, Nürnberg, Germany

    Nadine Gatzert

  2. 80803, Munich, Germany

    Gudrun Hoermann

  3. Institute of Insurance Economics, University of St. Gallen, Kirchlistrasse 2, 9010, St. Gallen, Switzerland

    Hato Schmeiser

Authors
  1. Nadine Gatzert
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  2. Gudrun Hoermann
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  3. Hato Schmeiser
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Correspondence to Hato Schmeiser.

Additional information

Nadine Gatzert and Hato Schmeiser gratefully acknowledge financial support by the Swiss National Science Foundation.

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Gatzert, N., Hoermann, G. & Schmeiser, H. Optimal rate classification for enhanced annuities. ZVersWiss 98, 565–577 (2010). https://doi.org/10.1007/s12297-009-0075-5

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