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Regular version of the site

Article

Survey on Scale functions for spectrally negative Levy processes

Science and Business: Ways of Development. 2018. Vol. 79. No. 1. P. 56-68.
Kelbert M., Karpikov I.

This article gives a brief summary on the main theoretical and practical results for the
Scale functions. The article is organized in the following way: the first part describes the main theoretical
concepts of Lévy processes, gives the formal definition and analytical properties of the Scale function.
The second part describes the most significant practical cases where the Scale functions are applied.
Thereafter, the closed-form expressions of Scale functions for several classes of spectrally negative Lévy
processes are considered. Finally, we concentrate on the very important application of Scale functions,
namely, derivation of the distribution of dividends, paid by the insurance company to shareholders. The
main contribution of this article is a lemma, describing the asymptotic behaviour of dividends, paid by n
identical companies.