The contemporary agriculture is among the most risky economic activities. In addition to the previously known production, price and market risk, and later also the financial risk, today agricultural producers are increasingly more often confronted with institutional risk and personnel management risk and risk related to climate change. On the other hand, farmers have at their disposal numerous tools and strategies to counteract threats and mitigate their negative effects. Among these risk management instruments and strategies, traditional/ conventional insurance of crops, livestock and tangible assets is still important. In this context, the basic goal of the article is to generalise the theoretical foundations of the above-mentioned insurance, but limited to their historically oldest approach; hence on the basis of neoclassical microeconomics and classical decision theory. According to the convention existing, the essence of the theory/hypothesis of the expected utility of von Neumann–Morgenstern is first analysed. In the last part of the article, the assumptions of the expected utility theory are concretised on the example of agricultural insurance.