Option pricing with hedging at fixed trading dates

We introduce trading restrictions in the well known Black-Scholes model and Cox-Ross-Rubinstein model, in the sense that hedging is only allowed at some fixed trading dates. As a consequence, the financial market is incomplete in both modified models. Applying Schweizer's (and Schal's) variance-optimal criterion for pricing and hedging general claims, we first analyse the dynamic consistency of the strategies which minimize the variance of the total loss due to hedging a given claim. Then we establish some convergence results, when the number of trading dates is either kept fixed or increases to infinity.