Local risk-minimization under transaction costs (Q2757552)

This paper proposes a new approach to the pricing and hedging of contingent claims under transaction costs in a general incomplete market in discrete time. Under the assumption of a bounded mean-variance tradeoff, substantial risk and nongeneracy condition on the conditional variance of asset returns, the existence of a locally risk-minimizing action (strategy) inclusive of transaction costs for every square-integrable contingent claim is proved. The robustness of local risk-minimization under the inclusion of transaction costs is shown. In particular, the results apply to any nondegenerate model with a finite state space if the transaction cost parameter is sufficiently small.