Numerical algorithms for Panjer recursion by applying Bernstein approximation

doi:10.1007/s11464-012-0230-5

Front Math Chin

2013, Vol. 8

Issue (5) : 1197-1226 https://doi.org/10.1007/s11464-012-0230-5

RESEARCH ARTICLE

Numerical algorithms for Panjer recursion by applying Bernstein approximation

Siyuan XIE¹, Jingping YANG²(

), Shulin ZHOU³

1. Department of Financial Mathematics, School of Mathematical Sciences, Peking University, Beijing 100871, China; 2. LMEQF, Department of Financial Mathematics, School of Mathematical Sciences and Center for Statistical Science, Peking University, Beijing 100871, China; 3. LMAM, School of Mathematical Sciences, Peking University, Beijing 100871, China

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Abstract

In actuarial science, Panjer recursion (1981) is used in insurance to compute the loss distribution of the compound risk models. When the severity distribution is continuous with density function, numerical calculation for the compound distribution by applying Panjer recursion will involve an approxi- mation of the integration. In order to simplify the numerical algorithms, we apply Bernstein approximation for the continuous severity distribution function and obtain approximated recursive equations, which are used for computing the approximated values of the compound distribution. The theoretical error bound for the approximation is also obtained. Numerical results show that our algorithm provides reliable results.

Keywords Compound risk model Panjer recursion Bernstein approximation excess-of-loss reinsurance

Corresponding Author(s): YANG Jingping,Email:yangjp@math.pku.edu.cn

Issue Date: 01 October 2013

Cite this article:

Siyuan XIE,Jingping YANG,Shulin ZHOU. Numerical algorithms for Panjer recursion by applying Bernstein approximation[J]. Front Math Chin, 2013, 8(5): 1197-1226.

URL:

https://academic.hep.com.cn/fmc/EN/10.1007/s11464-012-0230-5
https://academic.hep.com.cn/fmc/EN/Y2013/V8/I5/1197

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