Mathematics and Financial Economics

, Volume 13, Issue 2, pp 303–328 | Cite as

Characterizations of risk aversion in cumulative prospect theory

  • Tiantian Mao
  • Fan YangEmail author


In this paper, we investigate the necessary and sufficient conditions for a decision maker to be monotone risk averse and left-monotone risk averse, respectively, in cumulative prospect theory (CPT). Our results show that the decision maker is more pessimistic than greedy if she is either monotone or left-monotone risk averse, which is similar to that of Chateauneuf et al. (Econ Theory 25(3):649–667, 2005) in the rank-dependent expected utility model. Detailed examples are presented to illustrate the main theorems. With this work, we make a progress in the characterizations of risk aversion in CPT, which is essential in understanding the features of CPT and its applications in finance and insurance.


Monotone risk aversion Left-monotone risk aversion Dispersive order Location-independent risk order Loss aversion 

JEL Classification

C60 D81 G41 



Supports for Tiantian Mao from the NNSF of China (Grant Numbers: 71671176, 71871208, 11501575) are gratefully acknowledged. Support for Fan Yang from grant from the Natural Sciences and Engineering Research Council of Canada (Grant Number: 04242) is gratefully acknowledged.


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© Springer-Verlag GmbH Germany, part of Springer Nature 2018

Authors and Affiliations

  1. 1.Department of Statistics and FinanceUniversity of Science and Technology of ChinaHefeiChina
  2. 2.Department of Statistics and Actuarial ScienceUniversity of WaterlooWaterlooCanada

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