The principle of uncertain future: the probability of a future event contains a degree of (hidden) uncertainty. As a result, this uncertainty (in a sense, similar to vibrations, fluctuations) pushes the probability value back from the bounds to the middle of its range (from ~100% and ~0% to the...

This short paper is devoted to two items: 1) An analysis of Prelec’s weighting function at the probability p = 1 is highlighted (this analysis was performed by R. Duncan Luce in two articles with Ragnar Steingrimsson and János Aczél and here is referred to as the “Luce problem”). 2) The...

A possibility of the existence of a discontinuity of Prelec’s (probability weighting) function W(p) at the probability p = 1 is discussed. This possibility is supported by the Aczél–Luce question whether Prelec’s weighting function W(p) is equal to 1 at p = 1, by the purely mathematical...

A need for experiments on the certainty effect near the certainty (near the probability p = 1) is stated in this paper. The need supported by the Aczél–Luce question whether Prelec’s weighting function W(p) is equal to 1 at p = 1, by the purely mathematical restrictions and the...

The concept of unforeseen events is considered as a part of a hypothesis of uncertain future. The applications of the consequences of the hypothesis in utility and prospect theories are reviewed. Partially unforeseen events and their role in forecasting are analyzed. Preliminary preparations are...

Three main groups of results have been obtained: 1) The question is emphasized whether the probability weighting function W(p) is continuous. If W(p) reveals a discontinuity at p=1, then this is a topological feature. This can qualitatively change (at least) the mathematical aspects of the...

The report, that has been presented on the IX International Conference on Financial and Actuarial Mathematics, is devoted to the probability theory and economics. The theorems of existence of the ruptures near the borders of finite intervals and of the probability scale have been proved. The...

Arrangements (agreements, contracts, projects, etc.) are widespread economic events and are the fundamental concept of the economic theory. Infringements (breaches, modifications, changes, etc.) of arrangements are common and have a significant importance for the economic theory. For many years...

В статье показано, что возможность нарушения договоренностей существует для подавляющего большинства реальных договоренностей.

Доказана теорема о существовании разрывов в шкале вероятностей. Рассмотрены проявления этих разрывов в экономике и прогнозировании.