Pricing multi-asset barrier options

We obtain closed-form expressions for the exact no-arbitrage prices, as well as estimates, of some types of multivariate barrier options. A novelty for the estimates is that we combine ideas of convex analysis with tools of stochastic theory. The common aspect of all options herein is that the associated multivariate barriers are generated by hyperplanes placed on the collection (or vector) of stock prices, and not individually on each stock.