PATH DEPENDENT OPTIONS: HEDGING LOOKBACK OPTIONS AND PARTIAL LOOKBACK OPTIONS Hans-Peter Bermin, Nationalekonomiska institutionen, Lunds Universitet We consider a Black and Scholes economy with constant coefficients and give a short introcution to the theory of mathematical finance. We define the notations: no arbitrage, completeness, martingale measure, numeraires and hedging. Thereafter we show how to price and hedge contingent claims. Finally we use the Malliavin calculus approach to explicitly derive the hedging strategies of some well known contingent claims.