Option pricing by mathematical programming

Financial options typically incorporate times of exercise. Alternatively, they embody set-up costs or indivisibilities. Such features lead to planning problems with integer decision variables. Provided the sample space be finite, it is shown here that integrality constraints can often be relaxed. In fact, simple mathematical programming, aimed at arbitrage or replication, may find optimal exercise, and bound or identify option prices. When the asset market is incomplete, the bounds stem from non-linear pricing functionals.