Risk Management

, Volume 20, Issue 1, pp 77–94 | Cite as

The two-moment decision model with additive risks

  • Xu Guo
  • Andreas Wagener
  • Wing-Keung Wong
  • Lixing Zhu
Original Article


With multiple additive risks, the mean–variance approach and the expected utility approach of risk preferences are compatible if all attainable distributions belong to the same location–scale family. Under this proviso, we survey existing results on the parallels of the two approaches with respect to risk attitudes, the changes thereof, and the comparative statics for simple, linear choice problems under risks. In mean–variance approach all effects can be couched in terms of the marginal rate of substitution between mean and variance. We provide some simple proofs of some previous results. We apply the theory we stated or developed in our paper to study the behavior of banking firm and study risk-taking behavior with background risk in the mean–variance model.


Mean–variance model Location–scale family Background risk Multiple additive risks Expected utility approach 

JEL Classification

C0 D81 G11 



The authors are grateful to Professor Ira Horowitz for his valuable comments that have significantly improved this manuscript. The third author would like to thank Professors Robert B. Miller and Howard E. Thompson for their continuous guidance and encouragement. The authors are grateful to the Editor and two anonymous referees for constructive comments and suggestions that led to a significant improvement of an early manuscript. This research has been partially supported by the Fundamental Research Funds for the Central Universities, grants from the National Natural Science Foundation of China (11626130, 11601227, 11671042), Natural Science Foundation of Jiangsu Province, China (BK20150732), Asia University, Hang Seng Management College, Lingnan University, Shanghai University of International Business and Economics, Hong Kong Baptist University, the Research Grants Council (RGC) of Hong Kong (project numbers 12502814 and 12500915), and Ministry of Science and Technology (MOST), R.O.C.


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Copyright information

© Macmillan Publishers Ltd 2017

Authors and Affiliations

  • Xu Guo
    • 1
  • Andreas Wagener
    • 2
  • Wing-Keung Wong
    • 3
    • 4
    • 5
  • Lixing Zhu
    • 6
    • 7
  1. 1.School of StatisticsBeijing Normal UniversityBeijingChina
  2. 2.Institute of Economic PolicyUniversity of HannoverHannoverGermany
  3. 3.Department of Finance and Big Data Research CenterAsia UniversityTaichung CityTaiwan, ROC
  4. 4.Department of Economics and FinanceHang Seng Management CollegeHong KongChina
  5. 5.Department of EconomicsLingnan UniversityHong KongChina
  6. 6.School of Statistics and InformationShanghai University of International Business and EconomicsShanghaiChina
  7. 7.Department of MathematicsHong Kong Baptist UniversityHong KongChina

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