  We propose a hedging approach for general contingent claims when liquidity is
a concern and trading is subject to transaction cost. Multiple assets with
different liquidity levels are available for hedging. Our risk criterion
targets a tradeoff between minimizing the risk against fluctuations in the
stock price and incurring low liquidity costs. Following \c{C}etin U., Jarrow
R.A., and Protter P. (2004) we work in an arbitrage-free setting assuming a
supply curve for each asset. In discrete time, following the ideas in Schweizer
M. (1998) and Lamberton D., Pham H., Schweizer M. (1998) we prove the existence
of a locally risk-minimizing strategy under mild conditions on the price
process. Under stochastic and time-dependent liquidity risk we give a
closed-form solution for an optimal strategy in the case of a linear supply
curve model. Finally we show how our hedging method can be applied in energy
markets where futures with different maturities are available for trading. The
futures closest to their delivery period are usually the most liquid but
depending on the contingent claim not necessary optimal in terms of hedging. In
a simulation study we investigate this tradeoff and compare the resulting hedge
strategies with the classical ones.
