Fair pricing using deflators and decrement copulas: the unit linked endowment approach

SummaryThe Black-Scholes deflator and bivariate decrement copulas for the joint modeling of the time of death and time of withdrawal are used to determine the fair price of unit-linked endowment insurance contracts without or with a rising-floor guarantee. The fair fee income rate charged to the unit-linked fund is defined such that the present value of the fee income covers exactly the present value of the product guarantees and the expenses. In particular, a complete analytical treatment of the unit-linked endowment insurance without guarantee is presented.ZusammenfassungDerDeflator von Black-Scholes und spezifische Kopulas für die gemeinsame Modellierung der Ausscheideordnungen Tod und Rückkauf werden benützt, um den fairen Preis von fondsgebundenen Lebensversicherungen mit oder ohne Garantie zu bestimmen. Die faire Beitragsrate, welche dem Fonds belastet wird, wird durch folgende Bedingung definiert. Der diskontierte Wert der Beitragszahlungen deckt genau den diskontierten Wert der Garantie und der Kosten. Insbesondere wird eine vollständige analytische Behandlung der fondsgebundenen Lebensversicherung ohne Garantie vorgestellt.

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