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We consider a discrete-time financial model in a general sample space with penalty costs onshort positions. We consider a friction market closely related to the standard one except that withdrawalsfrom the portfolio value proportional to short positions are made. We provide necessary and sufficientconditions for the nonexistence of arbitrages in this situation and for a self-financing strategy to replicate acontingent claim. For the finite-sample space case, this result leads to an explicit and constructive procedurefor obtaining perfect hedging strategies.

Arbitrage-Free Conditions and Hedging Strategies for Markets withPenalty Costs on Short Positions