Analytical and computer simulation techniques for a stochastic model arising in discounting continuous uniform cash flows

Abstract

Present-value models are currently available for both single cash flows and continuous uniform cash flows under uncertain timing. Recent work by the authors has concentrated mainly on establishing theoretical results concerning the conditions under which unimodality will be introduced into the present-value distribution, particularly under exponential timing. Apart from the conventional (0) unimodality, there are two other forms of unimodality available which refer more to the nature of the unimodal behaviour rather than its location. When the timing mechanism operating for a continuous uniform cash flow is modelled by a geometrically distributed sum of exponential inter-assessment times, this paper establishes that the present-value distribution adopts a form of unimodality which is conceptually and structurally distinct from that form of unimodality adopted within the single cash flow analogue. Each present-value distribution will therefore become (0) unimodal under different prevailing economic conditions. One financial implication of these results is that it should be possible to develop coherent funding strategies for selecting a single cash flow option or a continuous uniform cash flow option having due regard to the current financial climate.