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

The 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 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.