@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",
doi = {10.3386/w6250},
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. "},
}