Aggregate dependent risks – risk measure calculation

• Authors: Heilpern Stanisław
• Languages of publication: EN

Abstracts

EN

We investigate the sum of dependent random variables. The dependent structure is modeled by copulas. The risk measures, VaR and ES of such sums, are calculated. We present the lower and upper border of VaR. The examples when the marginals have exponential and Pareto distribution are investigated. The influence of the degree of dependence on the value of VaR of the sum of dependent random variables is analysed.

Keywords

dependent random variables; copula; Frechet bounds; Value-at-Risk; expected shortfall

• Publisher: Wydawnictwo Uniwersytetu Ekonomicznego we Wrocławiu
• Journal: Mathematical Economics
• Year: 2011
• Issue: 7 (14)
• Pages: 107-122

Contributors

author

Heilpern Stanisław

References

• Alsina C. (1981). Some functional equation in the space of uniform distribution functions. Equationes Mathematicae. Vol. 22. Pp. 153-164.
• Artzner P., Delbaen F., Eber J., Heath D. (1999). Coherent measures of risk. Math. Finance. Vol. 9. Pp. 203-228.
• Denuit M., Genest C., Marceau E. (1999). Stochastic bounds on sums of dependent risks. Insurance: Math. Econ. Vol. 25. Pp. 85-104.
• Embrechts P., Hoing A., Puccetti G. (2005). Worst VaR scenarios. Math. Econ. Vol. 37. Pp. 115-134.
• Embrechts P., McNeil A., Straumann D. (2002). Correlation and dependence in risk management: Properties and pitfalls. In: M. Dempster (Ed.). Risk Management: Value at Risk and Beyond. Cambridge UP. Cambridge. Pp. 176-223.
• Heilpern S. (2007). Funkcje łączące. AE. Wrocław. Makarov G.D. (1981), Estimates for the distribution function of the sum of two random variables with given marginal distribution. Theory Probab. Appl. Vol. 26. Pp. 803-806.
• McNeil J.A., Frey R., Embrechts P. (2005). Quantitative Risk Management. Concepts, Techniques and Tools. Priceton UP. Priceton.
• Nelsen R.B. (1999). An Introduction to Copulas. Springer. New York.