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The distribution of a perpetuity, with applications to risk theory and pension funding. (English) Zbl 0743.62101
Let \(\{C_ k\mid k=1,2,3,\dots\}\) denote a stream of future cash flows, \(C_ k\) being the (random) amount to be paid at time \(k\). Let \(R_ k\) denote the (random) rate of return for the period \((k-1,k)\). Put \(S_ 0=0\). For \(k=1,2,3,\dots,\) consider the accumulated value, at time \(k\), of the first \((k-1)\) cash flows \(S_ k=(1+R_ k)(S_{k-1}+C_{k-1})\). Also, consider \[ Z_ k=(S_ k+C_ k)/(1+R_ 1)\dots(1+R_ k), \] which is the present value of the first \(k\) cash flows. The author studies the distributions of the stochastic processes \(\{S_ k\}\) and \(\{Z_ k\}\). Applications to risk theory and pension funding are also given.
Reviewer: E.Shiu (Winnipeg)

MSC:
62P05 Applications of statistics to actuarial sciences and financial mathematics
60G50 Sums of independent random variables; random walks
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