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Trade-off Between Robust Risk Measurement and Market Principles

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Abstract

Recently, it was shown that coherent risk measures are not robust with respect to changes in large data. On the other hand, in this article, we show that robust risk measures always generate pathological financial positions, Good Deals. This leaves a decision maker with a problem to either choose a robust risk measurement approach in a day-to-day real life decision making or an approach, which can correctly price financial products by considering the market principals such as No Good Deal assumption. In this paper, after stating clearly this problem, we propose a solution by introducing the minimal distribution-invariant modification of the risk measure, which does not produce any Good Deal and also is more robust comparing to the family of coherent risk measures.

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Notes

  1. In the literature it is also known as law-invariant.

  2. The reason is that Filipovic and Svindland [21] prove the canonical domain of any distribution-invariant coherent risk measure \(\rho \) can be extended to \(L^1\).

  3. It shows that, if someone enters the lottery, he/she should be payed by one or if he/she is risk averse by more than one dollar.

  4. For example unimodal distributions has this property.

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Authors and Affiliations

  1. Institute for Financial and Actuarial Mathematics, University of Liverpool, Room 218 Mathematical Sciences Building, Liverpool , L69 7ZL, United Kingdom

    Hirbod Assa

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  1. Hirbod Assa
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Correspondence to Hirbod Assa.

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Communicated by Moawia Alghalith.

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Assa, H. Trade-off Between Robust Risk Measurement and Market Principles. J Optim Theory Appl 166, 306–320 (2015). https://doi.org/10.1007/s10957-014-0593-8

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