IDEAS home Printed from https://ideas.repec.org/p/pra/mprapa/77625.html
   My bibliography  Save this paper

The Two-Moment Decision Model with Additive Risks

Author

Listed:
  • Guo, Xu
  • Wagener, Andreas
  • Wong, Wing-Keung
  • Zhu, Lixing

Abstract

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.

Suggested Citation

  • Guo, Xu & Wagener, Andreas & Wong, Wing-Keung & Zhu, Lixing, 2017. "The Two-Moment Decision Model with Additive Risks," MPRA Paper 77625, University Library of Munich, Germany.
    • Handle: RePEc:pra:mprapa:77625
    as

    Download full text from publisher

    File URL: https://mpra.ub.uni-muenchen.de/77625/1/MPRA_paper_77625.pdf
    File Function: original version
    Download Restriction: no
    ---><---

    Other versions of this item:

    References listed on IDEAS

    as
    1. Caballe, Jordi & Pomansky, Alexey, 1997. "Complete monotonicity, background risk, and risk aversion," Mathematical Social Sciences, Elsevier, vol. 34(3), pages 205-222, October.
    2. Thomas Eichner & Andreas Wagener, 2004. "Relative risk aversion, relative prudence and comparative statics under uncertainty: The case of (μ, σ)‐preferences," Bulletin of Economic Research, Wiley Blackwell, vol. 56(2), pages 159-170, April.
    3. Georges Dionne & Christian Gollier, 1992. "Comparative Statics Under Multiple Sources of Risk with Applications to Insurance Demand," The Geneva Risk and Insurance Review, Palgrave Macmillan;International Association for the Study of Insurance Economics (The Geneva Association), vol. 17(1), pages 21-33, June.
    4. Thomas Eichner & Andreas Wagener, 2005. "Notes and Comments: Measures of risk attitude: correspondences between mean-variance and expected-utility approaches," Decisions in Economics and Finance, Springer;Associazione per la Matematica, vol. 28(1), pages 53-65, June.
    5. Niu, Cuizhen & Wong, Wing-Keung & Xu, Qunfang, 2017. "Higher-Order Risk Measure and (Higher-Order) Stochastic Dominance," MPRA Paper 75948, University Library of Munich, Germany.
    6. Kimball, Miles S, 1990. "Precautionary Saving in the Small and in the Large," Econometrica, Econometric Society, vol. 58(1), pages 53-73, January.
    7. Haim Levy, 2004. "Prospect Theory and Mean-Variance Analysis," The Review of Financial Studies, Society for Financial Studies, vol. 17(4), pages 1015-1041.
    8. Broll, Udo & Guo, Xu & Welzel, Peter & Wong, Wing-Keung, 2015. "The banking firm and risk taking in a two-moment decision model," Economic Modelling, Elsevier, vol. 50(C), pages 275-280.
    9. Broll, Udo & Wahl, Jack E. & Wong, Wing-Keung, 2006. "Elasticity of risk aversion and international trade," Economics Letters, Elsevier, vol. 92(1), pages 126-130, July.
    10. Eichner, Thomas & Wagener, Andreas, 2014. "Insurance demand and first-order risk increases under (μ,σ)-preferences revisited," Finance Research Letters, Elsevier, vol. 11(4), pages 326-331.
    11. Meyer, Jack, 1987. "Two-moment Decision Models and Expected Utility Maximization," American Economic Review, American Economic Association, vol. 77(3), pages 421-430, June.
    12. Eeckhoudt, Louis & Gollier, Christian & Schlesinger, Harris, 1996. "Changes in Background Risk and Risk-Taking Behavior," Econometrica, Econometric Society, vol. 64(3), pages 683-689, May.
    13. Broll, Udo & Mukherjee, Soumyatanu, 2017. "International trade and firms' attitude towards risk," Economic Modelling, Elsevier, vol. 64(C), pages 69-73.
    14. Thomas Eichner, 2008. "Mean Variance Vulnerability," Management Science, INFORMS, vol. 54(3), pages 586-593, March.
    15. Jack Meyer, 1992. "Beneficial Changes in Random Variables Under Multiple Sources of Risk and Their Comparative Statics*," The Geneva Risk and Insurance Review, Palgrave Macmillan;International Association for the Study of Insurance Economics (The Geneva Association), vol. 17(1), pages 7-19, June.
    16. Wing-Keung Wong & Chenghu Ma, 2008. "Preferences over location-scale family," Economic Theory, Springer;Society for the Advancement of Economic Theory (SAET), vol. 37(1), pages 119-146, October.
    17. Eichner, Thomas & Wagener, Andreas, 2012. "Tempering effects of (dependent) background risks: A mean-variance analysis of portfolio selection," Journal of Mathematical Economics, Elsevier, vol. 48(6), pages 422-430.
    18. Günter Franke & Harris Schlesinger & Richard C. Stapleton, 2006. "Multiplicative Background Risk," Management Science, INFORMS, vol. 52(1), pages 146-153, January.
    19. Lars Tyge Nielsen & Fatma Lajeri, 2000. "Parametric characterizations of risk aversion and prudence," Economic Theory, Springer;Society for the Advancement of Economic Theory (SAET), vol. 15(2), pages 469-476.
    20. J. Tobin, 1958. "Liquidity Preference as Behavior Towards Risk," The Review of Economic Studies, Review of Economic Studies Ltd, vol. 25(2), pages 65-86.
    21. Sandmo, Agnar, 1971. "On the Theory of the Competitive Firm under Price Uncertainty," American Economic Review, American Economic Association, vol. 61(1), pages 65-73, March.
    22. Chamberlain, Gary, 1983. "A characterization of the distributions that imply mean--Variance utility functions," Journal of Economic Theory, Elsevier, vol. 29(1), pages 185-201, February.
    23. Thomas Eichner & Andreas Wagener, 2003. "Variance Vulnerability, Background Risks, and Mean-Variance Preferences," The Geneva Risk and Insurance Review, Palgrave Macmillan;International Association for the Study of Insurance Economics (The Geneva Association), vol. 28(2), pages 173-184, December.
    24. Alfred Müller & Marco Scarsini, 2001. "Stochastic Comparison of Random Vectors with a Common Copula," Mathematics of Operations Research, INFORMS, vol. 26(4), pages 723-740, November.
    25. Fatma Lajeri-Chaherli, 2004. "Proper and Standard Risk Aversion in Two-Moment Decision Models," Theory and Decision, Springer, vol. 57(3), pages 213-225, November.
    26. Ormiston, Michael B & Schlee, Edward E, 2001. "Mean-Variance Preferences and Investor Behaviour," Economic Journal, Royal Economic Society, vol. 111(474), pages 849-861, October.
    27. Choi, Gyemyung & Kim, Iltae & Snow, Arthur, 2001. "Comparative Statics Predictions for Changes in Uncertainty in the Portfolio and Savings Problems," Bulletin of Economic Research, Wiley Blackwell, vol. 53(1), pages 61-72, January.
    28. Wagener, Andreas, 2003. "Comparative statics under uncertainty: The case of mean-variance preferences," European Journal of Operational Research, Elsevier, vol. 151(1), pages 224-232, November.
    29. Cuizhen Niu & Wing-Keung Wong & Qunfang Xu, 2017. "Kappa ratios and (higher-order) stochastic dominance," Risk Management, Palgrave Macmillan, vol. 19(3), pages 245-253, August.
    30. Eichner, Thomas & Wagener, Andreas, 2011. "Increases in skewness and three-moment preferences," Mathematical Social Sciences, Elsevier, vol. 61(2), pages 109-113, March.
    31. Thomas Eichner & Andreas Wagener, 2003. "More on parametric characterizations of risk aversion and prudence," Economic Theory, Springer;Society for the Advancement of Economic Theory (SAET), vol. 21(4), pages 895-900, June.
    32. Thomas Eichner & Andreas Wagener, 2011. "Portfolio allocation and asset demand with mean-variance preferences," Theory and Decision, Springer, vol. 70(2), pages 179-193, February.
    33. Landsman, Zinoviy & Tsanakas, Andreas, 2006. "Stochastic ordering of bivariate elliptical distributions," Statistics & Probability Letters, Elsevier, vol. 76(5), pages 488-494, March.
    34. Pratt, John W & Zeckhauser, Richard J, 1987. "Proper Risk Aversion," Econometrica, Econometric Society, vol. 55(1), pages 143-154, January.
    35. Peter C. Fishburn & R. Burr Porter, 1976. "Optimal Portfolios with One Safe and One Risky Asset: Effects of Changes in Rate of Return and Risk," Management Science, INFORMS, vol. 22(10), pages 1064-1073, June.
    36. Wagener, Andreas, 2002. "Prudence and risk vulnerability in two-moment decision models," Economics Letters, Elsevier, vol. 74(2), pages 229-235, January.
    37. Lajeri-Chaherli, Fatma, 2004. "Proper prudence, standard prudence and precautionary vulnerability," Economics Letters, Elsevier, vol. 82(1), pages 29-34, January.
    38. Egozcue, Martín & García, Luis Fuentes & Wong, Wing-Keung & Zitikis, Ricardas, 2011. "Do investors like to diversify? A study of Markowitz preferences," European Journal of Operational Research, Elsevier, vol. 215(1), pages 188-193, November.
    39. Ilia Tsetlin & Robert L. Winkler, 2005. "Risky Choices and Correlated Background Risk," Management Science, INFORMS, vol. 51(9), pages 1336-1345, September.
    40. Broll, Udo & Egozcue, Martín & Wong, Wing-Keung & Zitikis, Ričardas, 2010. "Prospect theory and hedging risks," Dresden Discussion Paper Series in Economics 05/10, Technische Universität Dresden, Faculty of Business and Economics, Department of Economics.
    41. Thomas Eichner & Andreas Wagener, 2009. "Multiple Risks and Mean-Variance Preferences," Operations Research, INFORMS, vol. 57(5), pages 1142-1154, October.
    42. Fatma Lajeri-Chaherli, 2002. "More on Properness: The Case of Mean-Variance Preferences," The Geneva Risk and Insurance Review, Palgrave Macmillan;International Association for the Study of Insurance Economics (The Geneva Association), vol. 27(1), pages 49-60, June.
    43. Menezes, C F & Hanson, D L, 1970. "On the Theory of Risk Aversion," International Economic Review, Department of Economics, University of Pennsylvania and Osaka University Institute of Social and Economic Research Association, vol. 11(3), pages 481-487, October.
    44. W Henry Chiu, 2010. "Skewness Preference, Risk Taking and Expected Utility Maximisation," The Geneva Risk and Insurance Review, Palgrave Macmillan;International Association for the Study of Insurance Economics (The Geneva Association), vol. 35(2), pages 108-129, December.
    45. Hadar, Josef & Seo, Tae Kun, 1990. "The Effects of Shifts in a Return Distribution on Optimal Portfolios," International Economic Review, Department of Economics, University of Pennsylvania and Osaka University Institute of Social and Economic Research Association, vol. 31(3), pages 721-736, August.
    Full references (including those not matched with items on IDEAS)

    Citations

    Citations are extracted by the CitEc Project, subscribe to its RSS feed for this item.
    as


    Cited by:

    1. Nguyen Huu Hau & Tran Trung Tinh & Hoa Anh Tuong & Wing-Keung Wong, 2020. "Review of Matrix Theory with Applications in Education and Decision Sciences," Advances in Decision Sciences, Asia University, Taiwan, vol. 24(1), pages 28-69, March.
    2. Xiaoxia Huang & Guowei Jiang, 2021. "Portfolio management with background risk under uncertain mean-variance utility," Fuzzy Optimization and Decision Making, Springer, vol. 20(3), pages 315-330, September.
    3. Zhihui Lv & Amanda M. Y. Chu & Michael McAleer & Wing-Keung Wong, 2019. "Modelling Economic Growth, Carbon Emissions, and Fossil Fuel Consumption in China: Cointegration and Multivariate Causality," IJERPH, MDPI, vol. 16(21), pages 1-35, October.
    4. Chia-Lin Chang & Michael McAleer & Wing-Keung Wong, 2018. "Management Information, Decision Sciences, and Financial Economics: A Connection," Tinbergen Institute Discussion Papers 18-004/III, Tinbergen Institute.
    5. Raymond H. Chan & Ephraim Clark & Xu Guo & Wing-Keung Wong, 2020. "New development on the third-order stochastic dominance for risk-averse and risk-seeking investors with application in risk management," Risk Management, Palgrave Macmillan, vol. 22(2), pages 108-132, June.
    6. Zhihui Lv & Amanda M. Y. Chu & Wing Keung Wong & Thomas C. Chiang, 2021. "The maximum-return-and-minimum-volatility effect: evidence from choosing risky and riskless assets to form a portfolio," Risk Management, Palgrave Macmillan, vol. 23(1), pages 97-122, June.
    7. Richard Lu & Chen-Chen Yang & Wing-Keung Wong, 2018. "Time Diversification: Perspectives From The Economic Index Of Riskiness," Annals of Financial Economics (AFE), World Scientific Publishing Co. Pte. Ltd., vol. 13(03), pages 1-15, September.
    8. Chia-Lin Chang & Michael McAleer & Wing-Keung Wong, 2018. "Big Data, Computational Science, Economics, Finance, Marketing, Management, and Psychology: Connections," JRFM, MDPI, vol. 11(1), pages 1-29, March.
    9. Moawia Alghalith & Xu Guo & Cuizhen Niu & Wing-Keung Wong, 2017. "Input Demand Under Joint Energy and Output Prices Uncertainties," Asia-Pacific Journal of Operational Research (APJOR), World Scientific Publishing Co. Pte. Ltd., vol. 34(04), pages 1-12, August.
    10. Xu Guo & Raymond H. Chan & Wing-Keung Wong & Lixing Zhu, 2019. "Mean–variance, mean–VaR, and mean–CVaR models for portfolio selection with background risk," Risk Management, Palgrave Macmillan, vol. 21(2), pages 73-98, June.
    11. Chia-Lin Chang & Michael McAleer & Wing-Keung Wong, 2018. "Decision Sciences, Economics, Finance, Business, Computing, And Big Data: Connections," Advances in Decision Sciences, Asia University, Taiwan, vol. 22(1), pages 36-94, December.
    12. Wong, W.-K. & Lean, H.H. & McAleer, M.J. & Tsai, F.-T., 2018. "Why did Warrant Markets Close in China but not Taiwan?," Econometric Institute Research Papers EI2018-22, Erasmus University Rotterdam, Erasmus School of Economics (ESE), Econometric Institute.
    13. Alghalith, Moawia & Niu, Cuizhen & Wong, Wing-Keung, 2017. "The impacts of joint energy and output prices uncertainties in a mean-variance framework," MPRA Paper 79739, University Library of Munich, Germany.
    14. Kim-Hung Pho & Tuan-Kiet Tran & Thi Diem-Chinh Ho & Wing-Keung Wong, 2019. "Optimal Solution Techniques in Decision Sciences A Review," Advances in Decision Sciences, Asia University, Taiwan, vol. 23(1), pages 114-161, March.
    15. Chang, C-L. & McAleer, M.J. & Wong, W.-K., 2018. "Decision Sciences, Economics, Finance, Business, Computing, and Big Data: Connections," Econometric Institute Research Papers 18-024/III, Erasmus University Rotterdam, Erasmus School of Economics (ESE), Econometric Institute.
    16. Nadezhda Gribkova & Ričardas Zitikis, 2018. "A User-Friendly Algorithm for Detecting the Influence of Background Risks on a Model," Risks, MDPI, vol. 6(3), pages 1-11, September.
    17. Wing-Keung Wong & Hooi Hooi Lean & Michael McAleer & Feng-Tse Tsai, 2018. "Why Are Warrant Markets Sustained in Taiwan but Not in China?," Sustainability, MDPI, vol. 10(10), pages 1-17, October.
    18. Xu Guo & Xuejun Jiang & Wing-Keung Wong, 2017. "Stochastic Dominance and Omega Ratio: Measures to Examine Market Efficiency, Arbitrage Opportunity, and Anomaly," Economies, MDPI, vol. 5(4), pages 1-16, October.
    19. Huang, Xiaoxia & Yang, Tingting, 2020. "How does background risk affect portfolio choice: An analysis based on uncertain mean-variance model with background risk," Journal of Banking & Finance, Elsevier, vol. 111(C).
    20. Kim-Hung Pho & Thi Diem-Chinh Ho & Tuan-Kiet Tran & Wing-Keung Wong, 2019. "Moment Generating Function, Expectation And Variance Of Ubiquitous Distributions With Applications In Decision Sciences: A Review," Advances in Decision Sciences, Asia University, Taiwan, vol. 23(2), pages 65-150, June.
    21. Chia-Lin Chang & Michael McAleer & Wing-Keung Wong, 2018. "Big Data, Computational Science, Economics, Finance, Marketing, Management, and Psychology: Connections," Journal of Risk and Financial Management, MDPI, Open Access Journal, vol. 11(1), pages 1-29, March.

    Most related items

    These are the items that most often cite the same works as this one and are cited by the same works as this one.
    1. Vergara, Marcos & Bonilla, Claudio A., 2021. "Precautionary saving in mean-variance models and different sources of risk," Economic Modelling, Elsevier, vol. 98(C), pages 280-289.
    2. Fatma Lajeri-Chaherli, 2016. "On The Concavity And Quasiconcavity Properties Of ( Σ , Μ ) Utility Functions," Bulletin of Economic Research, Wiley Blackwell, vol. 68(3), pages 287-296, April.
    3. Guo, Xu & Wong, Wing-Keung & Zhu, Lixing, 2013. "Two-moment decision model for location-scale family with background asset," MPRA Paper 43864, University Library of Munich, Germany.
    4. Thomas Eichner & Andreas Wagener, 2009. "Multiple Risks and Mean-Variance Preferences," Operations Research, INFORMS, vol. 57(5), pages 1142-1154, October.
    5. Subhadip Mukherjee & Soumyatanu Mukherjee & Tapas Mishra & Udo Broll & Mamata Parhi, 2021. "Spot exchange rate volatility, uncertain policies and export investment decision of firms: a mean-variance decision approach," The European Journal of Finance, Taylor & Francis Journals, vol. 27(8), pages 752-773, May.
    6. Thomas Eichner, 2008. "Mean Variance Vulnerability," Management Science, INFORMS, vol. 54(3), pages 586-593, March.
    7. Eichner, Thomas & Wagener, Andreas, 2012. "Tempering effects of (dependent) background risks: A mean-variance analysis of portfolio selection," Journal of Mathematical Economics, Elsevier, vol. 48(6), pages 422-430.
    8. Thomas Eichner & Andreas Wagener, 2005. "Notes and Comments: Measures of risk attitude: correspondences between mean-variance and expected-utility approaches," Decisions in Economics and Finance, Springer;Associazione per la Matematica, vol. 28(1), pages 53-65, June.
    9. Subhadip Mukherjee & Soumyatanu Mukherjee & Tapas Mishra & Udo Broll, 2019. "Export investment under uncertainty: a mean-variance decision analysis for Indian manufacturing exporters," Discussion Papers 2019-18, University of Nottingham, GEP.
    10. Xu Guo & Raymond H. Chan & Wing-Keung Wong & Lixing Zhu, 2019. "Mean–variance, mean–VaR, and mean–CVaR models for portfolio selection with background risk," Risk Management, Palgrave Macmillan, vol. 21(2), pages 73-98, June.
    11. Alghalith, Moawia & Niu, Cuizhen & Wong, Wing-Keung, 2017. "The impacts of joint energy and output prices uncertainties in a mean-variance framework," MPRA Paper 79739, University Library of Munich, Germany.
    12. Moawia Alghalith & Xu Guo & Cuizhen Niu & Wing-Keung Wong, 2017. "Input Demand Under Joint Energy and Output Prices Uncertainties," Asia-Pacific Journal of Operational Research (APJOR), World Scientific Publishing Co. Pte. Ltd., vol. 34(04), pages 1-12, August.
    13. Thomas Eichner, 2010. "Slutzky equations and substitution effects of risks in terms of mean-variance preferences," Theory and Decision, Springer, vol. 69(1), pages 17-26, July.
    14. Thomas Eichner & Andreas Wagener, 2011. "Portfolio allocation and asset demand with mean-variance preferences," Theory and Decision, Springer, vol. 70(2), pages 179-193, February.
    15. Padhi, Sidhartha S. & Mukherjee, Soumyatanu & Edwin Cheng, T.C., 2024. "Optimal investment decision for industry 4.0 under uncertainties of capability and competence building for managing supply chain risks," International Journal of Production Economics, Elsevier, vol. 267(C).
    16. Chia-Lin Chang & Michael McAleer & Wing-Keung Wong, 2018. "Big Data, Computational Science, Economics, Finance, Marketing, Management, and Psychology: Connections," JRFM, MDPI, vol. 11(1), pages 1-29, March.
    17. Chia-Lin Chang & Michael McAleer & Wing-Keung Wong, 2018. "Decision Sciences, Economics, Finance, Business, Computing, and Big Data: Connections," Documentos de Trabajo del ICAE 2018-09, Universidad Complutense de Madrid, Facultad de Ciencias Económicas y Empresariales, Instituto Complutense de Análisis Económico.
    18. Chia-Lin Chang & Michael McAleer & Wing-Keung Wong, 2018. "Decision Sciences, Economics, Finance, Business, Computing, And Big Data: Connections," Advances in Decision Sciences, Asia University, Taiwan, vol. 22(1), pages 36-94, December.
    19. Guo, Xu & Wong, Wing-Keung & Zhu, Lixing, 2013. "An analysis of portfolio selection with multiplicative background risk," MPRA Paper 51331, University Library of Munich, Germany.
    20. Soumyatanu Mukherjee & Sidhartha S. Padhi, 2022. "Sourcing decision under interconnected risks: an application of mean–variance preferences approach," Annals of Operations Research, Springer, vol. 313(2), pages 1243-1268, June.

    More about this item

    Keywords

    Mean-variance model; location-scale family; background risk; multiple additive risks; expected-utility approach;
    All these keywords.

    JEL classification:

    • C0 - Mathematical and Quantitative Methods - - General
    • D81 - Microeconomics - - Information, Knowledge, and Uncertainty - - - Criteria for Decision-Making under Risk and Uncertainty
    • G11 - Financial Economics - - General Financial Markets - - - Portfolio Choice; Investment Decisions

    NEP fields

    This paper has been announced in the following NEP Reports:

    Statistics

    Access and download statistics

    Corrections

    All material on this site has been provided by the respective publishers and authors. You can help correct errors and omissions. When requesting a correction, please mention this item's handle: RePEc:pra:mprapa:77625. See general information about how to correct material in RePEc.

    If you have authored this item and are not yet registered with RePEc, we encourage you to do it here. This allows to link your profile to this item. It also allows you to accept potential citations to this item that we are uncertain about.

    If CitEc recognized a bibliographic reference but did not link an item in RePEc to it, you can help with this form .

    If you know of missing items citing this one, you can help us creating those links by adding the relevant references in the same way as above, for each refering item. If you are a registered author of this item, you may also want to check the "citations" tab in your RePEc Author Service profile, as there may be some citations waiting for confirmation.

    For technical questions regarding this item, or to correct its authors, title, abstract, bibliographic or download information, contact: Joachim Winter (email available below). General contact details of provider: https://edirc.repec.org/data/vfmunde.html .

    Please note that corrections may take a couple of weeks to filter through the various RePEc services.

    IDEAS is a RePEc service. RePEc uses bibliographic data supplied by the respective publishers.