ABSTRACT
In the complete financial market, every contingent claim can be hedged perfectly, and in an incomplete market, it is possible to stay on the safe side by super-hedging. In many situations, super-hedging needs a large amount of initial capital to set up the portfolio, which seems costly from the capital point of view. In this case, the following questions naturally arise. What if the investor is unwilling or unable to put up the large amount of initial capital required for hedging or super-hedging? Are we able to construct a hedging strategy so that the investor can achieve the maximal probability of a successful hedge with a smaller amount of initial capital? The answers can be fand with the help of quantile hedging.
