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A finite difference scheme for variational inequalities arising in stochastic control problems with several singular control variables

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  • Yoshioka, Hidekazu
  • Yaegashi, Yuta

Abstract

A finite difference scheme is developed for solving 1-D variational inequalities arising in stochastic control problems with several singular control variables. The scheme guarantees the uniqueness of numerical solutions. A policy iteration algorithm is then proposed to solve the discretized problem. The present approach is applied to solving variational inequalities associated to cost-effective management problems of benthic algae on the riverbed downstream of a dam: an urgent environmental problem. Accuracy of the scheme is verified to be first-order for both the solution and its free boundaries. An advanced problem that involves a max–min differential game structure is also examined. The scheme then computes reasonably accurate numerical solutions which are consistent with the theoretical asymptotic estimates.

Suggested Citation

  • Yoshioka, Hidekazu & Yaegashi, Yuta, 2019. "A finite difference scheme for variational inequalities arising in stochastic control problems with several singular control variables," Mathematics and Computers in Simulation (MATCOM), Elsevier, vol. 156(C), pages 40-66.
    • Handle: RePEc:eee:matcom:v:156:y:2019:i:c:p:40-66
    DOI: 10.1016/j.matcom.2018.06.013
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