Journal of Statistical Theory and Practice

, Volume 2, Issue 2, pp 253–277 | Cite as

Probability metrics with applications in finance

  • S. V. StoyanovEmail author
  • S. T. Rachev
  • F. J. Fabozzi


In the paper, we consider the application of the theory of probability metrics in several areas in the field of finance. First, we argue that specially structured probability metrics can be used to quantify stochastic dominance relations. Second, the methods of the theory of probability metrics can be used to arrive at a general axiomatic treatment of dispersion measures and probability metrics can be used to describe continuity of risk measures. Finally, the methods of probability metrics theory are applied to the benchmark-tracking problem significantly extending the problem setting.


probability metrics stochastic dominance dispersion measure deviation measure risk measure benchmark-tracking 

AMS Subject Classification



Unable to display preview. Download preview PDF.

Unable to display preview. Download preview PDF.


  1. Cambanis, S., Simons, G., Stout, W., 1976. Inequalities for Ek(X,Y) when the marginals are fixed, Z. Wahrsch. Verw. Geb. 36, 285–294.MathSciNetCrossRefGoogle Scholar
  2. Markowitz, H. M., 1952. Portfolio selection, Journal of Finance 7 (1), 77–91.Google Scholar
  3. Ortobelli, S., Rachev, S. T., Shalit, H., Fabozzi, F. J., 2007. Risk probability functionals and probability metrics applied to portfolio theory, working paper.Google Scholar
  4. Rachev, S. T., 1991. Probability Metrics and the Stability of Stochastic Models, Wiley, Chichester, U.K.zbMATHGoogle Scholar
  5. Rachev, S. T., Ortobelli, S., Stoyanov, S., Fabozzi, F. J., Biglova, A., 2008. Desirable properties of an ideal risk measure in portfolio theory, International Journal of Theoretical and Applied Finance 11 (1), 19–54.MathSciNetCrossRefGoogle Scholar
  6. Rockafellar, R. T., Uryasev, S., Zabarankin, M., 2006. Generalized deviations in risk analysis, Finance and Stochastics 10, 51–74.MathSciNetCrossRefGoogle Scholar
  7. Stoyanov, S., Rachev, S., Fabozzi, F., 2007. Probability metrics applied to problems in portfolio theory, Technical Report, Department of Econometrics and Statistics, University of Karlsruhe, Germany.Google Scholar
  8. Stoyanov, S., Rachev, S., Ortobelli, S., Fabozzi, F., 2008. Relative deviation metrics and the problem of strategy replication, Journal of Banking and Finance 32 (2), 199–206.CrossRefGoogle Scholar
  9. Szego, G., 2004. Risk Measures for the 21st Century, Wiley & Son Chichester.Google Scholar
  10. von Neumann, J., Morgenstern, O., 1944. Theory of Games and Economic Behavior, Princeton University Press, Princeton, New Jersey.zbMATHGoogle Scholar
  11. Zolotarev, V. M., 1997. Modern Theory of Summation of Random Variable, Brill Academic Publishers.CrossRefGoogle Scholar

Copyright information

© Grace Scientific Publishing 2008

Authors and Affiliations

  • S. V. Stoyanov
    • 1
    Email author
  • S. T. Rachev
    • 2
  • F. J. Fabozzi
    • 3
  1. 1.FinAnalytica, Inc.U.S.A. and University of Karlsruhe and Karlsruhe Institute of Technology (KIT)Germany
  2. 2.University of Karlsruhe and Karlsruhe Institute of Technology (KIT)Germany and University of California Santa BarbaraUSA
  3. 3.Yale School of ManagementUSA

Personalised recommendations