Buyer's quantile hedge portfolios in discrete-time trading

The problem of quantile hedging for American claims is studied from the perspective of the buyer of a contingent claim by minimizing the 'expected failure ratio'. After a general study of the problem in infinite-state spaces, we pass to finite dimensions and examine the properties of the resulting finite-dimensional optimization problems. In finite-state probability spaces we obtain a bilinear programming formulation that admits an exact linearization using binary exercise variables. Numerical results with S&P 500 index options demonstrate the computational viability of the formulations.