Adv. Math. Econ. 12, 153-166 (2009)

Some properties of distortion risk measures

Hideatsu Tsukahara

Department of Economics, Seijo University, 6–1–20 Seijo, Setagaya-ku, Tokyo 157-8511, Japan Received: January 16, 2008 Revised: July 17, 2008 JEL classification: C65, G19 Mathematical Subject Classification (2000): 60B05 Abstract. We give a simplified proof of the fact that law invariant convex risk measures 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 representation theorem of law invariant and comonotonically additive coherent risk measures, we prove that a coherent Key words: distortion, risk measure, stochastic order