DOI QR코드

DOI QR Code

A New Approach to Risk Comparison via Uncertain Measure

  • Li, Shengguo (School of Mathematics and Statistics, Huazhong Normal University) ;
  • Peng, Jin (Institute of Uncertain Systems, Huanggang Normal University)
  • Received : 2012.02.10
  • Accepted : 2012.04.23
  • Published : 2012.06.30

Abstract

This paper presents a new approach to risk comparison in uncertain environment. Based on the uncertainty theory, some uncertain risk measures and risk comparison rules are proposed. Afterward the bridges are built between uncertain risk measures and risk comparison rules. Finally, several comparable examples are given.

Keywords

References

  1. Artzner, P., Delbaen, F., Eber, J., and Heath, D. (1997), Thinking coherently, Risk, 10, 68-71.
  2. Barrett, G. F. and Donald, S. G. (2003), Consistent tests for stochastic dominance, Econometrica, 71, 71-104. https://doi.org/10.1111/1468-0262.00390
  3. Guldimann, T. M. (1995), Risk Metrics TM: Technical Document, JPMorgan, New York, NY.
  4. Lee, E. S. and Li, R.-J. (1988), Comparison of fuzzy numbers based on the probability measure of fuzzy events, Computers and Mathematics with Applications, 15, 887-896. https://doi.org/10.1016/0898-1221(88)90124-1
  5. Lee, L.-W. and Chen, S.-M. (2008), Fuzzy risk analysis based on fuzzy numbers with different shapes and different deviations, Expert Systems with Applications, 34, 2763-2771. https://doi.org/10.1016/j.eswa.2007.05.009
  6. Liu, B. (2007), Uncertainty Theory (2nd ed.), Springer, Berlin, Germany.
  7. Liu, B. (2009), Some research problems in uncertainty theory, Journal of Uncertain Systems, 3, 3-10.
  8. Liu, B. (2010a), Uncertainty Theory: A Branch of Mathematics for Modeling Human Uncertainty, Springer, Berlin, Germany.
  9. Liu, B. (2010b), Uncertain risk analysis and uncertain reliability analysis, Journal of Uncertain Systems, 4, 163-170.
  10. Markowitz, H. (1952), Portfolio selection, The Journal of Finance, 7, 77-91.
  11. Nojavan, M. and Ghazanfari, M. (2006), A fuzzy ranking method by desirability index, Journal of Intelligent and Fuzzy Systems, 17, 27-34.
  12. Peng, J. (2008), Measuring fuzzy risk by credibilistic value at risk, Proceedings of the 3rd International Conference on Innovative Computing Information and Control, Dalian, China, 270.
  13. Peng, J. (2009a), Value at risk and tail value at risk in uncertain environment, Proceedings of the 8th International Conference on Information and Management Sciences, Kunming, China, 787-793.
  14. Peng, J. (2009b), Average value at risk in fuzzy risk analysis, Advances in Intelligent and Soft Computing, 62, 1303-1313. https://doi.org/10.1007/978-3-642-03664-4_139
  15. Peng, J. and Li, S. (2010), Spectral measure of uncertain risk, Proceedings of the 1st International Conference on Uncertain Theory, Urumchi and Kashi, China, 1-7.
  16. Peng, J. and Li, S. (2011), Distortion risk measures of uncertain systems, Proceedings of the 9th International Conference on Reliability, Maintainability and Safety, Guiyang, China, 460-467.
  17. Peng, J., Jiang, Q., and Rao, C. (2007), Fuzzy dominance: a new approach for ranking fuzzy variables via credibility measure, International Journal of Uncertainty, Fuzziness and Knowledge-Based Systems, 15, 29-41. https://doi.org/10.1142/S0218488507004583
  18. Peng, J., Mok, H. M. K., and Tse, W.-M. (2005), Fuzzy dominance based on credibility distributions, Proceedings of the 2nd International Conference on Fuzzy Systems and Knowledge Discovery, Changsha, China, 295-303.
  19. Shaked, M. and Shanthikumar, J. G. (1994), Stochastic Orders and Their Applications, Academic Press, Boston, MA.
  20. Tran, L. and Duckstein, L. (2002), Comparison of fuzzy numbers using a fuzzy distance measure, Fuzzy Sets and Systems, 130, 331-341. https://doi.org/10.1016/S0165-0114(01)00195-6
  21. Zadeh, L. A. (1965), Fuzzy sets, Information and Control, 8, 338-353. https://doi.org/10.1016/S0019-9958(65)90241-X
  22. Zmeskal, Z. (2005), Value at risk methodology of international index portfolio under soft conditions (fuzzy- stochastic approach), International Review of Financial Analysis, 14, 263-275. https://doi.org/10.1016/j.irfa.2004.06.011

Cited by

  1. Two Uncertain Programming Models for Inverse Minimum Spanning Tree Problem vol.12, pp.1, 2013, https://doi.org/10.7232/iems.2013.12.1.009
  2. Efficient VaR and CVaR Measurement via Stochastic Kriging vol.28, pp.4, 2016, https://doi.org/10.1287/ijoc.2016.0705
  3. Uncertain expected utility function and its risk premium vol.28, pp.3, 2017, https://doi.org/10.1007/s10845-014-1007-3
  4. Uncertain Comprehensive Evaluation Method Based on Expected Value vol.2, pp.5, 2014, https://doi.org/10.1515/jssi-2014-0461