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Risk management under incomplete information: Exact upper and lower bounds for the Value at Risk

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  • DE SCHEPPER, Ann
  • HEIJNEN, Bart

Abstract

A key problem in financial and actuarial research, and particularly in the field of risk management, is the choice of models so as to avoid systematic biases in the measurement of risk. An alternative consists of working with incomplete information, by fixing only a number of parameters instead of a complete distribution, which results in bounds instead of unique results. In the present contribution, we derive upper and lower bounds for the Value at Risk , in case the information about the underlying distribution is restricted to successive moments, and possibly the mode. These bounds are obtained by means of a transformation of similar results about tail probabilities.

Suggested Citation

  • DE SCHEPPER, Ann & HEIJNEN, Bart, 2006. "Risk management under incomplete information: Exact upper and lower bounds for the Value at Risk," Working Papers 2006020, University of Antwerp, Faculty of Business and Economics.
    • Handle: RePEc:ant:wpaper:2006020
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    1. DE SCHEPPER, Ann & HEIJNEN, Bart, 2006. "Risk management under incomplete information: Exact upper and lower bounds for the probability to reach extreme values," Working Papers 2006019, University of Antwerp, Faculty of Business and Economics.
    2. Embrechts, Paul & Hoing, Andrea & Puccetti, Giovanni, 2005. "Worst VaR scenarios," Insurance: Mathematics and Economics, Elsevier, vol. 37(1), pages 115-134, August.
    3. Steven Vanduffel & Tom Hoedemakers & Jan Dhaene, 2005. "Comparing Approximations for Risk Measures of Sums of Nonindependent Lognormal Random Variables," North American Actuarial Journal, Taylor & Francis Journals, vol. 9(4), pages 71-82.
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    1. DE SCHEPPER, Ann & HEIJNEN, Bart, 2006. "Risk management under incomplete information: Exact upper and lower bounds for the probability to reach extreme values," Working Papers 2006019, University of Antwerp, Faculty of Business and Economics.

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    More about this item

    Keywords

    Risk management; Incomplete information; Value at Risk;
    All these keywords.

    JEL classification:

    • G14 - Financial Economics - - General Financial Markets - - - Information and Market Efficiency; Event Studies; Insider Trading
    • G22 - Financial Economics - - Financial Institutions and Services - - - Insurance; Insurance Companies; Actuarial Studies
    • C13 - Mathematical and Quantitative Methods - - Econometric and Statistical Methods and Methodology: General - - - Estimation: General
    • E40 - Macroeconomics and Monetary Economics - - Money and Interest Rates - - - General
    • C65 - Mathematical and Quantitative Methods - - Mathematical Methods; Programming Models; Mathematical and Simulation Modeling - - - Miscellaneous Mathematical Tools

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