Contingent claim valuation in a market with different interest rates

The problem of contingent claim valuation in a market with a higher interest rate for borrowing than for lending is discussed. The paper gives results which cover especially the European call and put options. The method used is based on transforming the problem to suitable auxiliary markets with only one interst rate for borrowing and lending and is adapted from a paper of Cvitanic and Karatzas where the authors study constrained portfolio problems.