Hostname: page-component-848d4c4894-nmvwc Total loading time: 0 Render date: 2024-06-29T04:24:57.288Z Has data issue: false hasContentIssue false
  • English
  • Français

Optimal Premium Plans for Reinsurance with Reinstatements

Published online by Cambridge University Press:  17 April 2015

Klaus TH. Hess  and
Klaus D. Schmidt
Klaus TH. Hess
Affiliation:
Lehrstuhl für Versicherungsmathemetik, Technische Universität Dresden, D-01062 Dresden. E-mail: schmidt@math.tu-dresden.de
Klaus D. Schmidt
Affiliation:
Lehrstuhl für Versicherungsmathemetik, Technische Universität Dresden, D-01062 Dresden. E-mail: schmidt@math.tu-dresden.de
Rights & Permissions [Opens in a new window]

Abstract

Core share and HTML view are not available for this content. However, as you have access to this content, a full PDF is available via the ‘Save PDF’ action button.

The present paper is concerned with optimal premium plans for a reinsurance contract with reinstatements. In the reinsurance contract considered here, constant reinstatement premiums are due when the reinsurer’s loss exceeds certain bounds. For this reinsurance contract we examine the existence of a premium plan which minimizes the expected squared difference between the loss and the total premium income of the reinsurer. We show that an optimal premium plan exists, that it is unique, and that it satisfies the net premium principle.

Type
Articles
Information
ASTIN Bulletin: The Journal of the IAA , Volume 34 , Issue 2 , November 2004 , pp. 299 - 313
Copyright
Copyright © ASTIN Bulletin 2004

References

Hess, K.TH. [2003] Das kollektive Modell der Risikotheorie in der Schadenexzedenten-Rückversicherung. Allg. Statist. Archiv 87, 309–320.Google Scholar
Hess, K.TH. and Schmidt, K.D. [2001] Credibility-Modelle in Tarifierung und Reservierung. Allg. Statist. Archiv 85, 225–246.Google Scholar
Mata, A.J. [2000] Pricing excess of loss reinsurance with reinstatements. ASTIN Bulletin 30, 349–368.10.2143/AST.30.2.504640CrossRefGoogle Scholar
Schmidt, K.D. [1996] Lectures on Risk Theory. Stuttgart: Teubner.10.1007/978-3-322-90570-3CrossRefGoogle Scholar
Schmidt, K.D. [2002] Versicherungsmathematik. Berlin-Heidelberg-New York, Springer.10.1007/978-3-662-10783-6CrossRefGoogle Scholar
Sundt, B. [1991] On excess of loss reinsurance with reinstatements. Mitt. Verein. Schweiz. Versicherungsmathematiker 91, 51–66.Google Scholar