Analytical and simulation techniques for discounting binomial random sums

Present-value models have often proved invaluable within the financial decision-making process. Such models are becoming increasingly more complex in their stochastic formulation and more sophisticated in their statistical objectives. Recent articles attempt to make exact inferences regarding the probability distribution of the present value. This paper establishes the result that whenever exponential timing is associated with the investment, then α-unimodality is automatically induced into the present-value distribution irrespective of the selection criteria of the components of that investment. Furthermore, the conditions leading to the familiar (0) unimodality are determined, whereby it often appears to be financially more prudent to delay the timing mechanism than to exercise caution in the selection of the components.