CALCULATING THE EXPECTATION AND VARIANCE OF THE PRESENT VALUE FOR A RANDOM PROFIT STREAM OF UNCERTAIN DURATION |
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Authors: | YIGAL GERCHAK THOMAS ÅSTEBRO |
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Institution: | University of Waterloo |
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Abstract: | We derive the mean and variance of the random discounted sum ![/></span> when <i>N</i>is uncertain, as are the <i>X<sub>n</sub>'s</i>. This quantity arises in applications involving random cash-flows over an uncertain number of years. One such application is R&D projects, where both the magnitude and duration of cash-flows are uncertain at the time of investment decision. Previous models have assumed cash-flow duration to be certain. We relax this assumption. We then specialize these results to geometric, mixed-geometric and Poisson distributions of the cash-flow duration.</td>
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