What is Pareto Optimality

A utility function is a tool used to assign numerical values to a set of goods or services in order to allow for a numerical representation of the preferences of a rational individual. Though its first use dates back to the 18th century, the term “utility” does not appear until the late 19th century in Welfare Economics, and it is fully axiomatised only in the mid-20th century with the birth of Decision Theory, where the utility function is the central concept. Indeed, in several studies focused, e.g., on analysing the roles of the rationality axioms and their weakening, or in completing partial preferences, a utility function is always considered to be the proper tool to fully depict the attitude of an investor toward risk.