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The Present Value of a Series of Cashflows: Convergence in a Random Environment

Published online by Cambridge University Press:  29 August 2014

Andrew J. G. Cairns
Andrew J. G. Cairns*
Affiliation:
Heriot-Watt University, Edinburgh, UK
*
Department of Actuarial Mathematics and Statistics, Heriot-Watt University, Riccarton, Edinburgh, EH14 4AS, UK.
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Abstract

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The present paper considers the present value, Z(t), of a series of cashflows up to some time t. More specifically, the cashflows and the interest rate process will often be stochastic and not necessarily independent of one another or through time. We discuss under what circumstances Z(t) will converge almost surely to some finite value as t→∞. This problem has previously been considered by Dufresne (1990) who provided a sufficient condition for almost sure convergence of Z(t) (the Root Test) and then proceeded to consider some specific examples of such processes. Here, we develop Dufresne's work and show that the sufficient condition for convergence can be proved to hold for quite a general class of model which includes the growing number of Office Models with stochastic cashflows.

Keywords

Stochastic discountingcashflow modelsalmost sure convergenceoffice model
Type
Articles
Information
ASTIN Bulletin: The Journal of the IAA , Volume 25 , Issue 2 , November 1995 , pp. 81 - 94
Copyright
Copyright © International Actuarial Association 1995

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