  Stochastic knapsack problem originally was a versatile model for controls in
telecommunication networks. Recently, it draws attentions of revenue management
community by serving as a basic model for allocating resources over time. We
develop approximation schemes for knapsack problems in this paper, a system of
nonlinear but solvable partial differential equations and stochastic partial
differential equation are shown to be the limit of the process that following
the optimal solution of the stochastic knapsack problem.
