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

Hao Li and Alexander Melnikov

Insurance: Mathematics and Economics, 2014, vol. 55, issue C, 250-260

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.

Keywords: Actuarial and financial models; Orthogonal polynomials; Rodrigues formula; Pearson’s equation (search for similar items in EconPapers)
Date: 2014
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Persistent link: https://EconPapers.repec.org/RePEc:eee:insuma:v:55:y:2014:i:c:p:250-260

DOI: 10.1016/j.insmatheco.2014.01.008

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