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Polynomial extensions of distributions and their applications in actuarial and financial modeling

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  • Li, Hao
  • Melnikov, Alexander

Abstract

The paper deals with orthogonal polynomials as a useful technique which can be attracted to actuarial and financial modeling. We use Pearson’s differential equation as a way for orthogonal polynomials construction and solution. The generalized Rodrigues formula is used for this goal. Deriving the weight function of the differential equation, we use it as a basic distribution density of variables like financial asset returns or insurance claim sizes. In this general setting, we derive explicit formulas for option prices as well as for insurance premiums. The numerical analysis shows that our new models provide a better fit than some previous actuarial and financial models.

Suggested Citation

  • Li, Hao & Melnikov, Alexander, 2014. "Polynomial extensions of distributions and their applications in actuarial and financial modeling," Insurance: Mathematics and Economics, Elsevier, vol. 55(C), pages 250-260.
    • Handle: RePEc:eee:insuma:v:55:y:2014:i:c:p:250-260
    DOI: 10.1016/j.insmatheco.2014.01.008
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    References listed on IDEAS

    as
    1. Furman, Edward & Zitikis, Ricardas, 2008. "Weighted premium calculation principles," Insurance: Mathematics and Economics, Elsevier, vol. 42(1), pages 459-465, February.
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    7. Cassidy, Daniel T. & Hamp, Michael J. & Ouyed, Rachid, 2010. "Pricing European options with a log Student’s t-distribution: A Gosset formula," Physica A: Statistical Mechanics and its Applications, Elsevier, vol. 389(24), pages 5736-5748.
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    Full references (including those not matched with items on IDEAS)

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