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1 results

  • Finite element approximations for stochastic control problems with unbounded state space

  • Part of
  • Martin G. Vieten, Richard H. Stockbridge
  • Journal:
    Journal of Applied Probability , First View
    Published online by Cambridge University Press:
    03 October 2024, pp. 1-28
    • Article
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  • A numerical method is proposed for a class of one-dimensional stochastic control problems with unbounded state space. This method solves an infinite-dimensional linear program, equivalent to the original formulation based on a stochastic differential equation, using a finite element approximation. The discretization scheme itself and the necessary assumptions are discussed, and a convergence argument for the method is presented. Its performance is illustrated by examples featuring long-term average and infinite horizon discounted costs, and additional optimization constraints.