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Risk management under incomplete information: Exact upper and lower bounds for the probability to reach extreme values

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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 present upper and lower bounds for tail probabilities or probabilities to reach extreme values, in case the information about the underlying distribution is restricted to successive moments, and possibly the mode. Part of these results were already published earlier, but we present them here in a uniform and clear way, and we add results for the case of three moments.

Suggested Citation

  • 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 Applied Economics.
  • Handle: RePEc:ant:wpaper:2006019
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    File URL: https://repository.uantwerpen.be/docman/irua/f3306c/01e89501.pdf
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    1. 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 Applied Economics.
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    Cited by:

    1. 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 Applied Economics.

    More about this item

    Keywords

    Risk management; Incomplete information; Tail probability; Extreme values;

    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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