Journal
OPERATIONS RESEARCH
Volume 49, Issue 3, Pages 372-397Publisher
INST OPERATIONS RESEARCH MANAGEMENT SCIENCES
DOI: 10.1287/opre.49.3.372.11218
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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 optimal-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 epsilon 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 epsilon -arbitrage strategies, we consider several numerical examples, including path-dependent options and options on assets with stochastic volatility and jumps.
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