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.
This is a preview of subscription content, log in via an institution.
Buying options
Tax calculation will be finalised at checkout
Purchases are for personal use only
Learn about institutional subscriptionsReferences
Calot, G., 1974. Curso de Estadística Descriptiva. Ed. Paraninfo, Madrid.
Cruz Rambaud, S., Maturo, F., Sánchez Pérez, A.M., 2015. Approach of the value of an annuity when non-central moments of the capitalization factor are known: an R application with interest rates following normal and beta distributions. Ratio Mathematica 28, 15–30.
Cruz Rambaud, S., Sánchez Pérez, A.M., 2016. Una aproximación del valor de una renta cuando el tipo de interés es aleatorio. XXIV Jornadas de Asepuma y XII Encuentro Internacional Granada (Spain), July 7–8.
Cruz Rambaud, S., Valls Martínez, M.C., 2002. La determinación de la tasa de actualización para la valoración de empresas. Análisis Financiero 87-2, 72–85.
Fisz, M., 1963. Probability Theory and Mathematical Statistics. John Wiley and Sons, Inc, New York.
Mira Navarro, J.C., 2014. Introducción a las Operaciones Financieras. Creative Commons, http://www.miramegias.com/emodulos/fileadmin/pdfs/mof.pdf.
Mood, A.M., Graybill, F.A., Boes, D.C., 1974. Introduction to the Theory of Statistics. 3rd Ed. Boston: McGraw Hill.
Rice, J.A., 2006. Mathematical Statistics and Data Analysis. 2nd Ed. California: Duxbury Press.
Suárez Suárez, A.S., 2005. Decisiones Óptimas de Inversión y Financiación en la Empresa. 2nd Ed. Madrid, Ed. Pirámide.
Villalón, J.G., Martínez Barbeito, J., Seijas Macías, J.A., 2009. Sobre la evolución de los tantos de interés. XVII Jornadas de Asepuma y V Encuentro Internacional 17, 1–502.
Author information
Authors and Affiliations
Corresponding author
Editor information
Editors and Affiliations
Rights and permissions
Copyright information
© 2017 Springer International Publishing AG
About this chapter
Cite this chapter
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
Download citation
DOI: https://doi.org/10.1007/978-3-319-54819-7_16
Published:
Publisher Name: Springer, Cham
Print ISBN: 978-3-319-54818-0
Online ISBN: 978-3-319-54819-7
eBook Packages: EngineeringEngineering (R0)