2Reliability and Risk

2.1. Risk: notion and measurement

2.1.1. Introductory notes

Various risks can accompany any person throughout his/her lifetime as well as all industrial, agricultural, financial organizations, public community, biological species, ecosystems and the whole of humanity. It can be said that every individual and all things are subject to risk. Most of the technical, economical, political, social and other decisions connected with risks that are inevitable arise due to uncertainness in different factors, influencing the phenomenon under decision.

Mathematical risk theory was designed and developed previously at the heart of actuarial and financial mathematics. Traditionally, the main problem of mathematical risk theory was concentrated around the ruin problem. However, the wider practical interests in risk evaluation other than insurance led to the sphere of interests in risk theory. Now risk theory has become a very fashionable subject not only in the traditional framework of applied mathematics, but also among different engineering, economical, financial, ecological and other specialties. More attention should be paid to the general notions of risk and its modeling.

Usually, risk is connected with a particular event and its consequences expressed in the form of some material or other losses or damages. In order to separate the common components and differences among various situations usually combined under the term “risk”, we formulate the term “risk”, ...

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