On the unimodality of present-value distributions

Financial literature in the past appears to have concentrated on developing present-value models, which were essentially deterministic. Even when stochastic formulations are presented, they are often directed towards the establishment of explicit formulae for mean value, variance and, in some cases, semi-variance. Alternative procedures, based on modal values or exact interval estimates for example, require more detailed analytical information regarding the structure of the underlying distribution function. The existence of a unique mode and its associated precision are two important aspects of this problem and both these questions can be addressed by a generalised concept of unimodality. Discounting random cash flows under exponential timing will inevitably lead to a present value, whose distribution is α-unimodal.