RISK AVERSION IN AN INCOMPLETE MARKET INFLUENCED BY GOVERNMENT REGULATION

Arrow and Pratt developed the risk aversion theory for utility functions. We present a novel framework in this paper: risk aversion in an incomplete market influenced by government regulation. The characteristics of an incomplete market and government regulation are described by sub-linear expectation theory and uncertainty theory, respectively. In this framework, we give the expressions of expectations of risk and prove Jensen's inequality. Then we introduce the risk premium, find its approximate value range, and prove Pratt's theorem in this case. Finally, a special type of risk aversion (decreasing risk aversion) and some operations that preserve decreasing risk aversion are given.