Rentenversicherung versus Fondsentnahmepläne, oder: Wie groß ist die Gefahr, den Verzehr des eigenen Vermögens zu überleben?

The present paper considers a retiree of a certain age (60 years, 70 years) facing the following alternative investment opportunities. One possibility is to buy a single premium immediate (constant) annuity-contract. This contract guarantees a life long pension payment of a certain amount, depending e.g. on the age of the retiree, the costs of the insurance company and the yield the company is able to realize from its capital investments. The alternative possibility is to invest the single premium into a mixture of stock and bond investment funds and to withdraw a certain (constant) amount periodically. The risk of the second opportunity is to outlive the income stream generated by this investment. The risk in this sense is specified by considering the probability of outliving one`s wealth. The determination of this probability is the central objective of the paper. It is assumed in the analysis that the amount of withdrawal from the fund is equivalent to the constant annuity of the insurance contract.