The paper focuses on modern analytical techniques for construction of utility functions over prizes, where the preferences of the decision maker are strictly increasing. If chosen and applied properly these methods facilitate the analysis and guarantee precise description of the decision makers’ preferences. The paper discusses modern analytical techniques, such as a modified arctg(.) form of the utility function, which contains prior information for the most typical risk attitude over lotteries, whose prizes can be both profits and losses. Also discussed is a power approximation of the utility.