Reducing or even eliminating a particular risk is an important task in risk management. However, often only imperfect hedging instruments are at hand, leading to *basis risk*. This is for instance the case if the asset that is hedged does not exactly coincide with the asset underlying the futures contract. A typical example for such a case is an airline company that wants to protect itself against changing kerosene prices. Since there is no liquid kerosene futures market the airline company may fall back on futures on less rened oil, such as crude oil futures, for hedging its kerosene risk. Another prominent example is an option on stock market indices such as the Dow Jones or DAX. Such options are often hedged by trading futures or forwards written on the index. In this case one of the difficulties to be mastered in practice is the possibly stochastic correlation between the underlying (index) and the hedging instrument (future).

**Selected Publications**

- Stefan Ankirchner, Peter Imkeller, Anton Popier,
*Optimal cross hedging of insurance derivatives*, Stochastic Anal. Appl., Vol.26, No. 4, 679-709, 2008
- Stefan Ankirchner, Peter Imkeller, Goncalo dos Reis,
*Pricing and hedging of derivatives based on non-tradable underlyings*, Math. Finance, Vol. 20, No. 2, 289 -312, 2010
- Stefan Ankirchner, Gregor Heyne,
*Cross hedging with stochastic correlation*, to appear in Finance and Stochastics, 2011
- Stefan Ankirchner, Georgi Dimitroff, Gregor Heyne, Christian Pigorsch,
*Futures Cross-hedging with a Stationary Basis*, to appear in Journal of Financial and Quantitative Analysis, 2011