PRICING EQUITY-LINKED LIFE-INSURANCE WITH ENDOGENOUS MINIMUM GUARANTEES

This paper analyses the problem of pricing insurance contracts in which the benefits are linked to the realization of a portfolio of equities and a minimum amount guaranteed is provided. Building on the models of Brennan and Schwartz (1976, 1979) and Delbaen (1990) for endowment policies, we extend them to the case in which the minimum guarantees are endogenous, i.e. they are functions of the premium(s) paid. In this framework we give sufficient conditions for both the single and the periodic premium to be well defined and present some significant examples of endogenous minimum guarantees satisfying these conditions. We also consider the problem of pricing insurance contracts different from the endowment one, and conclude with some numerical results.