Application of Probability and Possibility Theory in Investment Appraisal

There are two kinds of uncertainty the one which arises from the lack of knowledge (ignorance) and the other, which is due to randomness (variability). The majority of researchers agree that different types of uncertainty should be treated separately in risk analysis. This means that each type of uncertainty should be propagated through computation using an appropriate calculation method. If both types of uncertainty are present in a problem, then the appropriate methods must be combined into a single framework in order to obtain a single risk measure. Usually, as a result of such approach, a probability box (p-box) is obtained, which may be difficult to interpret for economic practitioners. In order to make a p-box useful from the practical point of view, in this article we propose methods to aggregate a p-box into a single cumulative distribution function. We demonstrate our approach on the example of the appraisal of an investment, where the distinction between different types of uncertainty is of great importance.