Small transaction cost asymptotics and dynamic hedging

Transaction costs are one of the major impediments to the implementation of dynamic hedging strategies. We consider an alternative to utility maximization, similar to the “good-deal” pricing framework in incomplete markets. We perform a dynamic risk–reward analysis for a family of non-self-financing strategies of practical importance: deterministic time hedging; i.e., hedging at predetermined, fixed, times. In the limit of small relative transaction costs, we carry out the asymptotic analysis and find that transaction costs affect the hedge ratios and that the time between trades is related in a simple way to the local sensitivities of the replication target.