Adv. Math. Econ. 9, 109-116 (2006)

The minimal risk of hedging with a convex risk measure

Yuji Umezawa

Graduate School of Mathematical Sciences, The University of Tokyo 3-8-1 Komaba, Meguro-ku, Tokyo 153-8914, Japan Received: July 28, 2005 Revised: December 20, 2005 JEL classification: D81 Mathematical Subject Classification (2000): 91B30 Abstract. We study the minimal hedging risk for a bounded European contingent claim when we use a convex risk measure. We find the infimum of hedging risk by using a kind of min-max theorem. Also we show that this infimum is again regarded as a convex risk measure. Key words: risk measure, hedging