Expected Present and Final Value of an Annuity when some Non-Central Moments of the Capitalization Factor are Unknown: Theory and an Application using R (original) (raw)

Abstract

The aim of this chapter is the development of three approaches for obtaining the value of an _n_-payment annuity, with payments of 1 unit each, when the interest rate is random. To calculate the value of these annuities, we are going to assume that only some non-central moments of the capitalization factor are known. The first technique consists in using a tetraparametric function which depends on the arctangent function. The second expression is derived from the so-called quadratic discounting whereas the third approach is based on the approximation of the mathematical expectation of the ratio of two random variables by Mood et al. (1974). A comparison of these methodologies through an application, using the R statistical software, shows that all of them lead to different results.

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Authors and Affiliations

1. Department of Economics and Business, University of Almería, Almería, Spain
   Salvador Cruz Rambaud & Ana María Sánchez Pérez
2. Department of Management and Business Administration, University of Chieti-Pescara, Chieti, Italy
   Fabrizio Maturo

Authors

1. Salvador Cruz Rambaud
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2. Fabrizio Maturo
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3. Ana María Sánchez Pérez
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Correspondence toSalvador Cruz Rambaud .

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Editors and Affiliations

1. Department of Mathematics and Physics, Faculty of Military Technology, University of Defence, Brno, Czech Republic
   Šárka Hošková-Mayerová
2. Department of Business Administration, University “G. d’Annunzio” of Chieti-Pescara, Pescara, Italy
   Fabrizio Maturo
3. Systems Research Institute, Polish Academy of Sciences, Warsaw, Poland
   Janusz Kacprzyk

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Cruz Rambaud, S., Maturo, F., Sánchez Pérez, A.M. (2017). Expected Present and Final Value of an Annuity when some Non-Central Moments of the Capitalization Factor are Unknown: Theory and an Application using R. In: Hošková-Mayerová, Š., Maturo, F., Kacprzyk, J. (eds) Mathematical-Statistical Models and Qualitative Theories for Economic and Social Sciences. Studies in Systems, Decision and Control, vol 104. Springer, Cham. https://doi.org/10.1007/978-3-319-54819-7\_16

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• DOI: https://doi.org/10.1007/978-3-319-54819-7\_16
• Published: 23 June 2017
• Publisher Name: Springer, Cham
• Print ISBN: 978-3-319-54818-0
• Online ISBN: 978-3-319-54819-7
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