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Dilatation monotone risk measures are law invariant

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Abstract

We prove that on an atomless probability space, every dilatation monotone convex risk measure is law invariant. This result, combined with the known ones, shows the equivalence between dilatation monotonicity and important properties of convex risk measures such as law invariance and second-order stochastic monotonicity.

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Authors and Affiliations

  1. Department of Probability Theory, Faculty of Mechanics and Mathematics, Moscow State University, 119992, Moscow, Russia

    Alexander S. Cherny

  2. Department of Mathematics, University of Leicester, Leicester, LE1 7RH, United Kingdom

    Pavel G. Grigoriev

Authors
  1. Alexander S. Cherny
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  2. Pavel G. Grigoriev
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Correspondence to Alexander S. Cherny.

Additional information

We would like to thank Johannes Leitner for helpful discussions. The second author made contributions to this paper while being affiliated to Heriot-Watt University and would like to express special thanks to Mark Owen, whose project (EPSRC grant no. GR/S80202/01) supported this research.

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Cherny, A.S., Grigoriev, P.G. Dilatation monotone risk measures are law invariant. Finance Stoch 11, 291–298 (2007). https://doi.org/10.1007/s00780-007-0034-8

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  • DOI: https://doi.org/10.1007/s00780-007-0034-8

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