@techreport{NBERw6250,
 title = "Pricing and Hedging Derivative Securities in Incomplete Markets: An E-Aritrage Model",
 author = "Dimitris Bertsimas and Leonid Kogan and Andrew W. Lo",
 institution = "National Bureau of Economic Research",
 type = "Working Paper",
 series = "Working Paper Series",
 number = "6250",
 year = "1997",
 month = "November",
 URL = "http://www.nber.org/papers/w6250",
 abstract = {Given a European derivative security with an arbitrary payoff function and a corresponding set of" underlying securities on which the derivative security is based, we solve the dynamic replication problem: find a" self-financing dynamic portfolio strategy involving only the underlying securities that most closely" approximates the payoff function at maturity.  By applying stochastic dynamic programming to the minimization of a" mean-squared-error loss function under Markov state-dynamics, we derive recursive expressions for the optimal-replication strategy that are readily implemented in practice.  The approximation error or " " of the optimal-replication strategy is also given recursively and may be used to quantify the "degree" of market incompleteness. " To investigate the practical significance of these  -arbitrage strategies examples including path-dependent options and options on assets with stochastic volatility and jumps. "},
}