Discretizing the State Space for High-Dimensional Continuous-State Stochastic Dynamic Programs

This paper describes a state space discretization scheme based on statistical experimental designs generated from orthogonal arrays of strength three with index unity. Chen et al. (1997) used this eecient discretization scheme to approximately solve high-dimensional continuous-state stochastic dynamic programming (SDP). Prior methods discretized the state space with a nite grid. The orthogonal array discretization reduced the growth in the number of discretization points from exponential to polynomial in the state space dimension, thus permitting a solution to higher-dimensional continuous-state SDP problems than previously possible. An orthogonal array design is a special subset of a full factorial experimental design. The orthogonal array designs are constructed using a result from Bose and Bush (1952), which involves the formation of a nondegenerate point conic in the nite projective plane. Relevant background on the projective plane is included to facilitate understanding of the orthogonal array construction.