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A note on positive supermartingales in ruin theory

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Blätter der DGVFM

Zusammenfassung

Die vorliegende Arbeit enthält einen elementaren Beweis der Kolmogorovschen Ungleichung für positive Supermartingale sowie eine Anwendung dieser Ungleichung auf das Ruin-Problem für eine Klasse von Reserve-Prozessen für die ein Anpassungskoeffizient nicht notwendigerweise existiert.

Summary

In this note, we present an elementary proof of Kolmogorov’s inequality for positive supermartingales and an application of this inequality to the ruin problem for a class of surplus processes for which an adjustment coefficient need to exist.

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References

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Authors and Affiliations

  1. Mannheim

    Klaus D. Schmidt

Authors
  1. Klaus D. Schmidt
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Schmidt, K.D. A note on positive supermartingales in ruin theory. Blätter DGVFM 19, 129–132 (1989). https://doi.org/10.1007/BF02809923

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  • DOI: https://doi.org/10.1007/BF02809923

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