Instruct: Identify the main and secondary category of Arxiv papers based on the titles and abstracts
Query: Approximating the Value Functions of Stochastic Knapsack Problems: A
  Homogeneous Monge-Amp\'ere Equation and Its Stochastic Counterparts   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.

16
The categories of this paper are: stat
30
The categories of this paper are: q-alg
37
The categories of this paper are: supr-con
35
The categories of this paper are: mtrl-th
36
The categories of this paper are: cmp-lg
31
The categories of this paper are: ao-sci
5
The categories of this paper are: gr-qc
26
The categories of this paper are: bayes-an
29
The categories of this paper are: funct-an
19
The categories of this paper are: eess
6
The categories of this paper are: astro-ph
8
The categories of this paper are: hep-ex
3
The categories of this paper are: physics
4
The categories of this paper are: cond-mat
34
The categories of this paper are: chem-ph
18
The categories of this paper are: econ