Recurrent methods of construction of cumulative functions of risk

Abstract


The estimation problem of the enterprise total losses related to the improper performance of liability is considered. The total losses distribution function and density for the aggregate contracts are constructed by the recurrent methods, proposed by N. de Pril and H. Panjer. The numerical experiments based on five groups of contract portfolio are carried out. The results analysis showing the advantages and disadvantages of calculating algorithms is made. In particular, the values of means at risk obtained by H. Panjer method are superior to the corresponding values founded by N. de Pril method, and the maximum value of loss occurrence probability in the distribution density realized by H. Panjer method is less than the one, gotten by N. de Pril method. The results can be used for the further development of N. de Pril and H. Panjer approaches for estimation of total losses of risk aggregate.

About the authors

Viktor N Nikishov

Samara State University

Email: tsh-sea05@yandex.ru
(к.ф.-м.н., доц.), доцент, каф. математики и бизнес-информатики; Самарский государственный университет; Samara State University

Elena V Mikhailova

Samara State University

Email: milena82@yandex.ru
аспирант, каф. математики и бизнес-информатики; Самарский государственный университет; Samara State University

References

  1. Гранатуров В. М. Экономический риск: сущность, методы измерерния, пути снижения. М.: Дело и сервис, 1999. 111 с.
  2. Севастьянов Б. А. Курс теории вероятностей и математической статистики. М.: Наука, 1982. 256 с.
  3. De Pril N. On the exact computation of the aggregate claims distribution in the individual life model // Astin Bulletin, 1986. Vol. 16, no. 2. Pp. 109-112.
  4. De Pril N. The aggregate claims distribution in the individual model with arbitrary positive claims // Astin Bulletin, 1989. Т. 19, № 1. С. 9-24.
  5. Фалин Г. И. Математический анализ рисков в страховании. Москва: Российский юридический издательский дом, 1994. 130 с.
  6. Королев В. Ю., Бенинг В. Е., Шоргин С. Я. Математические основы теории риска. М.: Физматлит, 2007. 544 с.
  7. Panjer H. H. Recursive evaluation of a famaly of compound distributions // Astin Bulletin, 1981. Vol. 12, no. 1. Pp. 12-26.

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