The theorem of existence of the ruptures in the probability scale was proved in 2010. The theorem is used to analyze and to partially answer to the basic questions of insurance. The question is “To insure or not”. The goal of this paper is to reveal pure mathematical aspects of insurance...

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...

Ideal economics? A “non-ideal” economics approach has been proposed, which considers the possibility of arrangement infringements. It gives promises for both solving fundamental problems of economic theory and creation of new directions and fields of research. The approach application in...

The definition of arrangement infringement has been given. Several characteristics of hurricanes as large-scale events and objectives for the first stages of insurance data analysis have been sketched out. Scale hypotheses, insurance and investment problems have been formulated.

A new mathematical direction is presented. Sub-interval analysis is a simple and effective tool for practical and theoretical calculations and estimations. Feasible applications of sub-interval analysis include economics (accounting, auditing, microeconomics, macroeconomics, banking, insurance,...