Pricing derivative securities in incomplete markets
WSC '04 Proceedings of the 36th conference on Winter simulation
Hedging with a correlated asset: Solution of a nonlinear pricing PDE
Journal of Computational and Applied Mathematics
Optimal Control and Hedging of Operations in the Presence of Financial Markets
Mathematics of Operations Research
Tracking a Financial Benchmark Using a Few Assets
Operations Research
Securitization and Real Investment in Incomplete Markets
Management Science
Numerical solution of a parabolic problem arising in finance
Applied Numerical Mathematics
| Hi-index | 0.00 |
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 "e" 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 e-arbitrage strategies, we consider several numerical examples, including path-dependent options and options on assets with stochastic volatility and jumps.