Partial means in the economic risk analysis of projects

Partial means constitute a new measure of economic risk that unifies and subsumes many less general measures. The partial mean of a random variable is its expected value conditioned on its falling within a given range. For a random variable such as the present worth of a return with uncertain timings, partial means are directly usable to discretize a continuum of outcomes in order to build a decision tree. More importantly, partial means can be used as building blocks in computing a variety of established risk measures - loss integrals, Fishbum's risk measure, the expected value of perfect information - thus unifying these measures and elucidating their interrelationships. In this paper we define partial means and related measures, illustrate their characteristics through numerical examples, and show their relationships to several less general risk measures. Tables of partial mean properties are presented for various probability distributions, to facilitate computations and comparisons among competing measures of risk.