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

Document Type

Conference Proceeding

Publication Date

7-2-2018

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.

Identifier

85062599584 (Scopus)

ISBN

[9781538665725]

Publication Title

Proceedings Winter Simulation Conference

External Full Text Location

https://doi.org/10.1109/WSC.2018.8632477

ISSN

08917736

First Page

1802

Last Page

1813

Volume

2018-December

Grant

CMMI-1537322

Fund Ref

National Science Foundation

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