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

Masaya Kannari, Riu Naito, Toshihiro Yamada*

*Corresponding author for this work

Research output: Contribution to journalArticlepeer-review

Abstract

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.

Original languageEnglish
Article number119
JournalEntropy
Volume26
Issue number2
DOIs
StatePublished - 2024/02

Keywords

  • Monte Carlo simulation
  • asymptotic expansion
  • relative entropy
  • stochastic optimization
  • weak approximation

ASJC Scopus subject areas

  • Information Systems
  • Mathematical Physics
  • Physics and Astronomy (miscellaneous)
  • General Physics and Astronomy
  • Electrical and Electronic Engineering

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