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Modeling the Conditional Dependence between Discrete and Continuous Random Variables with Applications in Insurance

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  • Emilio Gómez-Déniz

    (Department of Quantitative Methods and TIDES Institute, Campus de Tafira s/n, University of Las Palmas de Gran Canaria, 35017 Las Palmas de Gran Canaria, Spain)

  • Enrique Calderín-Ojeda

    (Centre for Actuarial Studies, Department of Economics, The University of Melbourne, 3010 Victoria, Australia)

Abstract

We jointly model amount of expenditure for outpatient visits and number of outpatient visits by considering both dependence and simultaneity by proposing a bivariate structural model that describes both variables, specified in terms of their conditional distributions. For that reason, we assume that the conditional expectation of expenditure for outpatient visits with respect to the number of outpatient visits and also, the number of outpatient visits expectation with respect to the expenditure for outpatient visits is related by taking a linear relationship for these conditional expectations. Furthermore, one of the conditional distributions obtained in our study is used to derive Bayesian premiums which take into account both the number of claims and the size of the correspondent claims. Our proposal is illustrated with a numerical example based on data of health care use taken from Medical Expenditure Panel Survey (MEPS), conducted by the U.S. Agency of Health Research and Quality.

Suggested Citation

  • 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.
    • Handle: RePEc:gam:jmathe:v:9:y:2020:i:1:p:45-:d:469193
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    References listed on IDEAS

    as
    1. Spanos,Aris, 1999. "Probability Theory and Statistical Inference," Cambridge Books, Cambridge University Press, number 9780521424080.
    2. Sarabia, José María & Gómez-Déniz, Emilio & Vázquez-Polo, Francisco J., 2004. "On the Use of Conditional Specification Models in Claim Count Distributions: an Application to Bonus-Malus Systems," ASTIN Bulletin, Cambridge University Press, vol. 34(1), pages 85-98, May.
    3. Frangos, Nicholas E. & Vrontos, Spyridon D., 2001. "Design of Optimal Bonus-Malus Systems With a Frequency and a Severity Component On an Individual Basis in Automobile Insurance," ASTIN Bulletin, Cambridge University Press, vol. 31(1), pages 1-22, May.
    4. 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.
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