Joint work with Thomas F. Coleman, Yuying Li and Cristina Patron

In an incomplete market, it is impossible to eliminate the intrinsic risk of an option that cannot be replicated. Thus it is unclear what are the

optimal hedging stratey and fair value of an option. Quadratic risk minimization is often used to determine fair value and hedging strategy for an option when the market is incomplete. We investigate hedging strategies and prices from alternative piecewise linear risk minimization. We illustrate that piecewise linear risk minimization often leads to smaller expected total hedging cost and significantly different, possibly more desirable, hedging strategies from that of the quadratic risk minimization. Comparative numerical results are provided for discrete dynamic hedging.