Comparing Quadratic and Non-Quadratic Local Risk Minimization for the Hedging of Contingent Claims

Abstract

In this note, I study further a new approach recently introduced for the hedging of derivatives in incomplete markets via non quadratic local risk minimization. A structure result is provided, which essentially shows the equivalence between non-quadratic risk minimization under the historical probability and quadratic local risk minimization under an equivalent, implicitly defined probability.