Abstract
In the present paper a theoretical approach to rate making in excess of loss reinsurance with reinstatement is discussed. This approach is founded on the models and methods of risk theory and in particular on the theory of premium calculation principles. Reinstatement premiums, however, are dependent on the losses occurred and paid by the reinsurer, and are consequently random unlike the usual premiums in direct and reinsurance. Therefore the standard approach of applying premium calculation principles has to be modified appropriately. This is demonstrated here particularly for premium calculation principles based on a utility function and on a loss function approach. In most cases, however, an explicit premium formula cannot be derived. Therefore numerical techniques are applied to obtain premiums in the case that the underlying claim size and claim number distributions are known.
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DIENST, H.-R., ed. (1988), Mathematische Verfahren der Rückversicherung, Verlag Versicherungswirtschaft, Karlsruhe.
GERATHEWOHL, K. (1980), Reinsurance. Principles and Practice, Vol. I, Verlag Versicherungswirtschaft, Karlsruhe.
GERATHEWOHL, K. (1982), Reinsurance. Principles and Practice, Vol. II, Verlag Versicherungswirtschaft, Karlsruhe.
HEILMANN, W.-R. (1988), Fundamentals of Risk Theory, Verlag Versicherungswirtschaft, Karlsruhe.
PFEIFFER, C. (1986), Einführung in die Rückversicherung, 3rd ed., Gabler, Wiesbaden.
SANDLEBEN, W.-C. (1991), Risikotheoretische Modelle für die „ Wiederaujfüllung“in der Rückversicherung, Diploma Thesis, University of Karlsruhe.
SUNDT, B. (1990), On Excess of Loss Reinsurance with Reinstatements, Actuarial Research Report 18, Storebrand, Oslo.
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© 1993 Springer-Verlag Berlin · Heidelberg
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Heilmann, WR., Sandleben, WC. (1993). On the Rating of Excess of Loss Reinsurance Treaties with Reinstatement. In: Diewert, W.E., Spremann, K., Stehling, F. (eds) Mathematical Modelling in Economics. Springer, Berlin, Heidelberg. https://doi.org/10.1007/978-3-642-78508-5_50
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DOI: https://doi.org/10.1007/978-3-642-78508-5_50
Publisher Name: Springer, Berlin, Heidelberg
Print ISBN: 978-3-642-78510-8
Online ISBN: 978-3-642-78508-5
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