The theorem of existence of the ruptures in probability scale and the basic question of insurance

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 processes and to analyze these aspects by pure mathematical methods, including application of the theorem. Its most significant result: when uncertainty increases, then taking the theorem into account may reverse insurant’s and insurer’s decisions to the opposite ones.