Some properties of exact ruin probability for Erlang-distributed claims

Authors

  • Sergey S. Vallander St. Petersburg State University, Universitetskaya nab., 7-9, St. Petersburg, 199034, Russian Federation;

Abstract

We discuss analytic structure of exact expression for ruin probability in classical Cram`er-Lundberg model with Erlang-distributed claims. This formula can be easily received via standard Laplace transform method. Nevertheless its fine structure depends crucially on the absence (presence) of multiple roots of some polynomial equation. We prove that all roots of this equation are simple (have multiplicity one). As a consequence the ruin probability represents as a linear combination of pure exponents (complex exponents in general case). Refs 3.

Keywords:

ruin probability, Erlang-distributed claims

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Published

2015-02-01

How to Cite

Vallander, S. S. (2015). Some properties of exact ruin probability for Erlang-distributed claims. Vestnik of Saint Petersburg University. Mathematics. Mechanics. Astronomy, 2(1), 34–36. Retrieved from https://math-mech-astr-journal.spbu.ru/article/view/11127

Issue

Vol. 2 No. 1 (2015)

Section

Mathematics

License

Articles of "Vestnik of Saint Petersburg University. Mathematics. Mechanics. Astronomy" are open access distributed under the terms of the License Agreement with Saint Petersburg State University, which permits to the authors unrestricted distribution and self-archiving free of charge.