Quantile hedging and efficient hedging
Lenneke Roodenburg, November 7, 2001
An complete arbitrage-free models contingent claims can be hedged perfectly.
This means that the risk of losing money can be eliminated. However this
also implies the vanishing of all profits. It is not always possible to make
a perfect hedge in an incomplete financial model, but one can still stay on
the safe side by using a superhedge strategy. The amount of starting capital
one needs for carrying out such a superhedge strategy is very high. So it is
clear that in practice perfect hedge strategies as well as superhedge
strategies can not always be used. That is why certain partial hedge
strategies are developed. I will treat two of such partial hedges: quantile
hedging and efficient hedging. With quantile hedging a strategy will be
constructed which maximizes the probability on a succesful hedge given a
constraint on the starting capital and with efficient hedging a strategy
will be constructed which is efficient with respect to the risk of losing a
certain amount of money and the necessary starting capital.
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Last Updated: October 16, 2001