The aim of the paper is to analyze the performance of a portfolio of participating life annuities, focusing on the minimum acceptable income level throughout the quantiles of the return distribution. The model, in addition to the necessary consideration of the volatility of financial markets, gives a central role to the impact of the longevity phenomenon.

Variable annuities are investment products offered by Insurance Companies. They allow investors to place assets in mutual funds under the umbrella of a tax-deferred account. The account value of variable annuities fluctuates based on the performance of the selected mutual funds and therefore some risks are involved. Recently there has been a growing interest in using fuzzy numbers to deal with financial uncertainty.