An optimal multi-step quadratic risk-adjusted hedging strategy

An optimal multi-step hedging strategy is proposed to minimize one’s exposure to risk. The proposed strategy, called the QRA-hedging, is based on the minimization of the quadratic risk-adjusted hedging costs and extends the result of Elliott and Madan (1998) to the multi-step case. The multi-step QRA-hedging cost is proved to be the same as the no-arbitrage price derived by the extended Girsanov principle. The QRA-hedging strategy is investigated under complete and incomplete market models. A regression-based method is proposed to estimate the QRA-hedging positions. And a dynamic programming is developed to facilitate computation of the QRA-hedging strategy. Simulation and empirical studies are performed to compare the QRA with other hedging strategies under complete and incomplete market models.