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Risk Theory with Affine Dividend Payment Strategies

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Number Theory – Diophantine Problems, Uniform Distribution and Applications

Abstract

We consider a classical compound Poisson risk model with affine dividend payments. We illustrate how both by analytical and probabilistic techniques closed-form expressions for the expected discounted dividends until ruin and the Laplace transform of the time to ruin can be derived for exponentially distributed claim amounts. Moreover, numerical examples are given which compare the performance of the proposed strategy to classical barrier strategies and illustrate that such affine strategies can be a noteworthy compromise between profitability and safety in collective risk theory.

Dedicated to Robert F. Tichy at the occasion of his 60th birthday

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Notes

  1. 1.

    In this way, a practically motivated question of insurance risk theory leads to non-trivial mathematical problems and relations, a connection which is also in the tradition of Robert Tichy’s work, to whom this paper is dedicated. For the application of Quasi-Monte Carlo results to risk theory by Robert Tichy, see, e.g., [3, 28].

  2. 2.

    In fact, there is some methodological link to a calculation in Tichy [29], where for a horizontal dividend barrier an explicit calculation for V without ruin was given.

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Acknowledgements

Financial support by the Swiss National Science Foundation Project 200020 143889 is gratefully acknowledged.

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Authors and Affiliations

  1. University of Lausanne and Swiss Finance Institute, Quartier UNIL-Dorigny, Bâtiment Extranef, 1015, Lausanne, Switzerland

    Hansjörg Albrecher

  2. University of Lausanne, Quartier UNIL-Dorigny, Bâtiment Extranef, 1015, Lausanne, Switzerland

    Arian Cani

Authors
  1. Hansjörg Albrecher
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  2. Arian Cani
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Correspondence to Hansjörg Albrecher .

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Editors and Affiliations

  1. Institute of Analysis and Number Theory, Graz University of Technology, Graz, Austria

    Christian Elsholtz

  2. Institute of Analysis and Number Theory, Graz University of Technology, Graz, Austria

    Peter Grabner

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Albrecher, H., Cani, A. (2017). Risk Theory with Affine Dividend Payment Strategies. In: Elsholtz, C., Grabner, P. (eds) Number Theory – Diophantine Problems, Uniform Distribution and Applications. Springer, Cham. https://doi.org/10.1007/978-3-319-55357-3_2

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