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A Primer in Understanding Retirement Planning with Fuzzy Mathematics
Irini Dimitriyadis and Cengiz Kahraman

This paper aims at studying welfare at retirement by analyzing the functioning of a private pension system. A person enters a private pension plan on a purely voluntary basis, makes regular investments into a fund and is free to choose out of a set of investment alternatives. The amount of savings produced during the accumulation phase depends solely on the level of contributions and the riskiness of the investment portfolio chosen. When the person becomes eligible for a pension, he may draw the fund in a lump sum, he may invest all or part of his savings to buy a life annuity or may choose to invest or consume it in any other way he desires. Welfare at retirement depends highly on the capability of the individual to correctly match his decisions during the accumulation phase with his expectations in retirement. He has to evaluate correctly the sufficiency of the fund at hand, follow a prudent spending policy so that he is not out of money at late retirement. Concepts such as the riskiness of the portfolio, the sufficiency of the money at hand or the evaluation of longevity are fuzzy concepts and may be better defined as “low”, “medium” or “high” rather than with exact numerical values. We try to give the basic notions of the retirement problem by fuzzifying the level of contributions, the investment rate of return and life length, trying to create a series of “possible” outcomes depending on a range of decisions of the individual to show the way towards prudent decisions.

Keywords: Pensions, annuities, fuzzy numbers, money’s worth, longevity

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