BFS 2002

Contributed Talk

Hedging American call options with insufficient initial funds

Shlomo Levental, Anatolli V. Skorohod

We deal with the minimal initial investment that is needed to hedge an American option when one is allowed to fail with positive probability. We develop general formulas for the problem and give a sharp answer in the case of call options in the Black-Scholes model. Bounds are provided in the general submartingale case. Finally we present a general result on optimal stopping in a restricted setup.