Dynamic Hedging in Incomplete Markets: A Simple Solution

We provide fully analytical, optimal dynamic hedges in incomplete markets by employing the traditional minimum-variance criterion. Our hedges are in terms of generalized "Greeks" and naturally extend no-arbitrage--based risk management in complete markets to incomplete markets. Whereas the literature characterizes either minimum-variance static, myopic, or dynamic hedges from which a hedger may deviate unless able to precommit, our hedges are time-consistent. We apply our results to derivatives replication with infrequent trading and determine hedges and replication values, which reduce to generalized Black-Scholes expressions in specific settings. We also investigate dynamic hedging with jumps, stochastic correlation, and portfolio management with benchmarking. The Author 2012. Published by Oxford University Press on behalf of The Society for Financial Studies. All rights reserved. For Permissions, please e-mail: journals.permissions@oup.com., Oxford University Press.