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Mathematical Problems in Engineering
Volume 2012 (2012), Article ID 937324, 20 pages
Research Article

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

Departamento de Engenharia de Telecomunicações e Controle, Escola Politécnica da Universidade de São Paulo, 05508-900 São Paulo, SP, Brazil

Received 25 October 2011; Accepted 13 December 2011

Academic Editor: Weihai Zhang

Copyright © 2012 O. L. V. Costa and E. V. Queiroz Filho. This is an open access article distributed under the Creative Commons Attribution License, which permits unrestricted use, distribution, and reproduction in any medium, provided the original work is properly cited.


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