Abstract
Pricing and hedging life insurance with guarantees is a major concern of insurers and researchers. In this paper, we use the generalized Fourier analysis for pricing and hedging that proves to be fast and accurate. For hedging we use a local risk minimization and pseudo di erential operators to give a concise formula for the hedging ratio. An important problem we address is that hedging has to be solved in the historical world while pricing is done in the risk-neutral world. We apply this procedure to the Guarantees for Maturity Bene t, Minimum Death Bene t, and the Minimum Accumulated Bene t.