Solutions and diagnostics of switching problems with linear state dynamics

Authors

  • Juri Hinz University of Technology Sydney
  • Nicholas Yap University of Technology Sydney

DOI:

https://doi.org/10.21914/anziamj.v57i0.8855

Keywords:

Markov decisions, approximate dynamic programming, stochastic control, duality

Abstract

Optimal control problems of stochastic switching type appear frequently when making decisions under uncertainty and are notoriously challenging from a computational viewpoint. Although numerous approaches have been suggested in the literature to tackle them, typical real-world applications are inherently high dimensional and usually drive common algorithms to their computational limits. Furthermore, even when numerical approximations of the optimal strategy are obtained, practitioners must apply time-consuming and unreliable Monte Carlo simulations to assess their quality. In this paper, we show how one can overcome both difficulties for a specific class of discrete-time stochastic control problems. A simple and efficient algorithm which yields approximate numerical solutions is presented and methods to perform diagnostics are provided. doi:10.1017/S1446181115000279

Published

2016-04-09

Issue

Section

Special Issue for Financial Mathematics, Probability and Statistics