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

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  • Cairns, Andrew J. G.

Abstract

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.

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  • Cairns, Andrew J. G., 1995. "The Present Value of a Series of Cashflows: Convergence in a Random Environment," ASTIN Bulletin, Cambridge University Press, vol. 25(2), pages 81-94, November.
    • Handle: RePEc:cup:astinb:v:25:y:1995:i:02:p:81-94_00
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    Cited by:

    1. Date, P. & Mamon, R. & Wang, I.C., 2007. "Valuation of cash flows under random rates of interest: A linear algebraic approach," Insurance: Mathematics and Economics, Elsevier, vol. 41(1), pages 84-95, July.
    2. Date, P. & Mamon, R. & Jalen, L. & Wang, I.C., 2010. "A linear algebraic method for pricing temporary life annuities and insurance policies," Insurance: Mathematics and Economics, Elsevier, vol. 47(1), pages 98-104, August.

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