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A Class of Conjugate Priors for Log‐Normal Claims Based on Conditional Specification

Author

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  • José María Sarabia
  • Enrique Castillo
  • Emilio Gómez‐Déniz
  • Francisco J. Vázquez‐Polo

Abstract

In this article, a new methodology for obtaining a premium based on a broad class of conjugate prior distributions, assuming lognormal claims, is presented. The new class of prior distributions arise in a natural way, using the conditional specification technique introduced by Arnold, Castillo, and Sarabia (1998, 1999). The new family of prior distributions is very flexible and contains, as particular cases, many other distributions proposed in the literature. Together with its flexibility, the main advantage of this distribution is that, due to its dependence on a large number of hyperparameters, it allows incorporating a wide amount of prior information. Several methods for hyperparameter elicitation are proposed. Finally, some examples with real and simulated data are given.

Suggested Citation

  • José María Sarabia & Enrique Castillo & Emilio Gómez‐Déniz & Francisco J. Vázquez‐Polo, 2005. "A Class of Conjugate Priors for Log‐Normal Claims Based on Conditional Specification," Journal of Risk & Insurance, The American Risk and Insurance Association, vol. 72(3), pages 479-495, September.
    • Handle: RePEc:bla:jrinsu:v:72:y:2005:i:3:p:479-495
    DOI: 10.1111/j.1539-6975.2005.00133.x
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    Cited by:

    1. Sarabia, José María & Guillén, Montserrat, 2008. "Joint modelling of the total amount and the number of claims by conditionals," Insurance: Mathematics and Economics, Elsevier, vol. 43(3), pages 466-473, December.
    2. Emilio Gómez-Déniz & Enrique Calderín-Ojeda, 2020. "Modeling the Conditional Dependence between Discrete and Continuous Random Variables with Applications in Insurance," Mathematics, MDPI, vol. 9(1), pages 1-15, December.

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