Alternative Hedging in a Discrete-Time Incomplete Market

Abstract

We present an alternative approach to hedging in incomplete markets. A corresponding alternative risk-minimization algorithm that identifies an optimal hedging portfolio consistent with initial capital and an investor-chosen risk criterion is developed. Having been introduced in earlier works by Josephy et al, it is adapted here to facilitate a comparison with both quadratic and piece wise linear local risk-minimization approaches reported in the work of Coleman et al. Numerical results establish that the alternative approach is competitive and frequently better than the local risk-minimization approaches. Various quantitative and qualitative comparisons are made between the local risk-minimization approaches and our alternative hedging approach.