Quantile Hedging by Hans F¨ollmer and Peter Leukert

 Humboldt-Universitat zu Berlin

Abstract. In a complete financial market every contingent claim can be hedged perfectly. In an incomplete market it is possible to stay on the safe side by superhedging. But such strategies may require a large amount of initial capital. Here we study the question what an investor can do who is unwilling to spend that much, and who is ready to use a hedging strategy which succeeds with high probability.

Introduction

The problem of pricing and hedging of contingent claims is well understood in the context of arbitrage-free models which are complete. In such models every contingent claim is attainable, i.e., it can be replicated by a self-financing trading strategy. The cost of replication defines the price of the claim, and it can be computed as the expectation of the claim under the unique equivalent martingale measure.



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