Probability metrics with applications in finance
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.
Key-wordsprobability metrics stochastic dominance dispersion measure deviation measure risk measure benchmark-tracking
AMS Subject Classification91B28
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- Markowitz, H. M., 1952. Portfolio selection, Journal of Finance 7 (1), 77–91.Google Scholar
- 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
- 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
- Szego, G., 2004. Risk Measures for the 21st Century, Wiley & Son Chichester.Google Scholar