Revenue management has become an important tool in the airline, hotel, and rental car industries. We describe asymptotic properties of revenue management policies derived from the solution of a deterministic optimization problem. Our primary results state that, within a stochastic and dynamic framework, solutions arising out of a single well-known linear program can be used to generate allocation policies for which the normalized revenue converges in distribution to a constant upper bound on the optimal value. We also show similar asymptotic results for expected revenues. In addition, we describe counterintuitive behavior that can occur when allocations are updated during the booking process (updating allocations can lead to lower expected revenue). These results add to the understanding of allocation policies and help to make concrete the statement that simple policies from easy-to-solve formulations can be relatively effective, even when analyzed in the more realistic stochastic and dynamic framework.