Using regenerative simulation to calibrate exponential approximations to risk measures of hitting times to rarely visited sets

Peter W. Glynn, Marvin K. Nakayama, Bruno Tuffin

Research output: Chapter in Book/Report/Conference proceedingConference contribution

Abstract

We develop simulation estimators of risk measures associated with the distribution of the hitting time to a rarely visited set of states of a regenerative process. In various settings, the distribution of the hitting time divided by its expectation converges weakly to an exponential as the rare set becomes rarer. This motivates approximating the hitting-time distribution by an exponential whose mean is the expected hitting time. As the mean is unknown, we estimate it via simulation. We then obtain estimators of a quantile and conditional tail expectation of the hitting time by computing these values for the exponential approximation calibrated with the estimated mean. Similarly, the distribution of the sum of lengths of cycles before the one hitting the rare set is often well-approximated by an exponential, and we analogously exploit this to estimate the two risk measures of the hitting time. Numerical results demonstrate the effectiveness of our estimators.

Original languageEnglish (US)
Title of host publicationWSC 2018 - 2018 Winter Simulation Conference
Subtitle of host publicationSimulation for a Noble Cause
PublisherInstitute of Electrical and Electronics Engineers Inc.
Pages1802-1813
Number of pages12
ISBN (Electronic)9781538665725
DOIs
StatePublished - Jan 31 2019
Event2018 Winter Simulation Conference, WSC 2018 - Gothenburg, Sweden
Duration: Dec 9 2018Dec 12 2018

Publication series

NameProceedings - Winter Simulation Conference
Volume2018-December

Conference

Conference2018 Winter Simulation Conference, WSC 2018
CountrySweden
CityGothenburg
Period12/9/1812/12/18

All Science Journal Classification (ASJC) codes

  • Software
  • Computer Science Applications
  • Modeling and Simulation

Cite this

Glynn, P. W., Nakayama, M. K., & Tuffin, B. (2019). Using regenerative simulation to calibrate exponential approximations to risk measures of hitting times to rarely visited sets. In WSC 2018 - 2018 Winter Simulation Conference: Simulation for a Noble Cause (pp. 1802-1813). [8632477] (Proceedings - Winter Simulation Conference; Vol. 2018-December). Institute of Electrical and Electronics Engineers Inc.. https://doi.org/10.1109/WSC.2018.8632477