A Study of Risk Preference: The Shape of Utility Functions for Three Different Types of Risk

Purpose : Risk-averse preferences are widespread in society, exemplified by the prevalence of insurance. The existence of risk aversion is explained by the concave shape of the utility function. Simultaneously, risk-seeking behaviors, such as purchasing lottery tickets and horse tickets, are also widely observed, suggesting that utility is represented by a convex function. Many ideas have been proposed to reconcile this apparent contradiction, but it has not yet been completely resolved. This study proposes a framework to solve the difficulty of utility functions associated with a mixture of risk aversion and risk-seeking. Additionally, based on this framework, we consider the suitability of the transfer by insurance in accordance with the type of risk.
Research design, data, methodology : Based on previous studies, we focus on the necessity of using different utility functions for different types of risks to explain the coexistence of risk-averse and risk-seeking preferences. We devise three classifications according to the nature of risk and attempt to resolve the above difficulties.
Results : The results show that diverse risk preferences can be qualitatively explained by categorizing risk into three types: pure, speculative, and lottery risks, and by applying concave, somewhat linear, and convex utility functions to each of them. Additionally, we distinguish between risks that affect assets and liabilities, which affect income and expenses, and show that the former are more compatible with insurance.
Conclusions : The fact that the utility function is not linear suggests that utility is determined not by logic but by perception. Therefore, to understand people's preferences, it is necessary to understand the conditions of judgment based on perception. Since pure, speculative, and lottery risks are perceived as risks of different nature, it is appropriate to apply different utility functions to each of them.