A NOTE ON ARBITRAGE AND CLOSED CONVEX CONES

Walter Schachermayer

Mathematical Finance, 2005, vol. 15, issue 1, 183-189

Abstract: We give an example of a subspace Kof such that , where denotes the closure with respect to convergence in probablity. On the other hand, the cone C≔K−L∞+ is dense in L∞ with respect to the weak‐star topology σ(L∞, L1). This example answers a question raised by I. Evstigneev. The topic is motivated by the relation of the notion of no arbitrage and the existence of martingale measures in Mathematical Finance.

Date: 2005
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