Abstract
We give a simplified proof of the fact that law invariant convex risk mea sures automatically have Fatou property, which is first shown by Jouini et al. (Adv. Math. Econ. 9:49–71, 2006). After providing a streamlined proof of Kusuoka's rep resentation theorem of law invariant and comonotonically additive coherent risk mea sures, we prove that a coherent distortion risk measures preserves some well-known stochastic orders.
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Tsukahara, H. (2009). Some properties of distortion risk measures. In: Kusuoka, S., Maruyama, T. (eds) Advances in Mathematical Economics. Advance in Mathematical Economics, vol 12. Springer, Tokyo. https://doi.org/10.1007/978-4-431-92935-2_6
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DOI: https://doi.org/10.1007/978-4-431-92935-2_6
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