This paper presents results on the convergence for hedging strategies in the setting of incomplete financial markets. We examine the convergence of the so-called locally risk-minimizing strategy. It is proved that such a choice for the trading strategy, when perfect hedging of contingent claims is infeasible, is robust under weak convergence. Several fundamental examples extracted from the financial modelling literature illustrate this property for both deterministic and random time intervals shrinking to zero.

Keywords : Weak convergence; incomplete financial markets; locally risk-minimizing strategy; hedging strategy; minimal martingale measure.

AMS 1991 Subject Classification: 60F05; 60G44; 90A09.