Entropy (Jan 2024)

Asymptotic Expansion and Weak Approximation for a Stochastic Control Problem on Path Space

  • Masaya Kannari,
  • Riu Naito,
  • Toshihiro Yamada

DOI
https://doi.org/10.3390/e26020119
Journal volume & issue
Vol. 26, no. 2
p. 119

Abstract

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The paper provides a precise error estimate for an asymptotic expansion of a certain stochastic control problem related to relative entropy minimization. In particular, it is shown that the expansion error depends on the regularity of functionals on path space. An efficient numerical scheme based on a weak approximation with Monte Carlo simulation is employed to implement the asymptotic expansion in multidimensional settings. Throughout numerical experiments, it is confirmed that the approximation error of the proposed scheme is consistent with the theoretical rate of convergence.

Keywords