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On annuities under random rates of interest


  • Krzysztof Burnecki
  • Agnieszka Marciniuk
  • Aleksander Weron


In the article we consider accumulated values of annuities-certain with yearly payments with independent random interest rates. We focus on general annuities with payments varying in arithmetic and geometric progression which are important basic varying annuities (see Kellison, 1991). They are equivalent to the types studied recently by Zaks (2001). We derive, via recursive relationships, mean and variance formulae of the final values of the annuities. As a consequence, we obtain the moments related to the already discussed cases, which leads to a correction of main results from Zaks (2001).

Suggested Citation

  • Krzysztof Burnecki & Agnieszka Marciniuk & Aleksander Weron, 2002. "On annuities under random rates of interest," HSC Research Reports HSC/02/01, Hugo Steinhaus Center, Wroclaw University of Technology.
  • Handle: RePEc:wuu:wpaper:hsc0201

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    File Function: Second revision, 20 Dec 2002
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    Cited by:

    1. Rafal Weron, 2002. "Pricing European options on instruments with a constant dividend yield: The randomized discrete-time approach," HSC Research Reports HSC/02/04, Hugo Steinhaus Center, Wroclaw University of Technology.
    2. Agnieszka Marciniuk, 2021. "Equity Release Contracts with Varying Payments," Prague Economic Papers, Prague University of Economics and Business, vol. 2021(5), pages 552-574.

    More about this item


    Finance mathematics; Annuity; Accumulated value; Random interest rate;
    All these keywords.

    JEL classification:

    • G13 - Financial Economics - - General Financial Markets - - - Contingent Pricing; Futures Pricing
    • G22 - Financial Economics - - Financial Institutions and Services - - - Insurance; Insurance Companies; Actuarial Studies


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