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The Pearson system of utility functions
Affiliation:1. School of Computer and Software, Nanjing University of Information Science and Technology, China;2. School of Computer Science and Electrical Engineering, University of Essex, Colchester CO4 3SQ, UK;3. School of Computer Science, The University of Nottingham, Nottingham NG8 1BB, UK;4. Department of Applied Mathematics, China Jiliang University, Hangzhou, ZheJiang 310018, China;5. Faculty of Engineering and Science, University of Greenwich, Kent ME4 4TB, UK;1. Department of Mechanical Engineering, Tezpur University, 784028 India;2. Department of Mechanical Engineering, Indian Institute of Technology Guwahati, 781039 Indian;1. School of Economics and Management, Chongqing University of Posts and Telecommunications, Chongqing, 400065, China;2. College of Management and Economics, Tianjin University, Tianjin, 300072, China;3. Business School, Nankai University, Tianjin, 300071, China;4. School of Computer Science and Engineering, University of Electronic Science and Technology of China, 611731, China;5. Big Data Research Center, University of Electronic Science and Technology of China, 611731, China
Abstract:This paper describes a parametric family of utility functions for decision analysis. The parameterization embeds the HARA class in a four-parameter representation for the risk aversion function. The resulting utility functions can have only four shapes: concave, convex, S-shaped, and reverse S-shaped. This makes the family suited for both expected utility and prospect theory. The paper also describes an alternative technique to estimate the four parameters from elicited utilities, which is simpler than standard fitting by minimization of the mean quadratic error.
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