TY - GEN

T1 - Using regenerative simulation to calibrate exponential approximations to risk measures of hitting times to rarely visited sets

AU - Glynn, Peter W.

AU - Nakayama, Marvin K.

AU - Tuffin, Bruno

N1 - Funding Information:
This work has been supported in part by the National Science Foundation under Grant No. CMMI-1537322. Any opinions, findings, and conclusions or recommendations expressed in this material are those of the authors and do not necessarily reflect the views of the National Science Foundation.

PY - 2019/1/31

Y1 - 2019/1/31

N2 - 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.

AB - 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.

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U2 - 10.1109/WSC.2018.8632477

DO - 10.1109/WSC.2018.8632477

M3 - Conference contribution

AN - SCOPUS:85062599584

T3 - Proceedings - Winter Simulation Conference

SP - 1802

EP - 1813

BT - WSC 2018 - 2018 Winter Simulation Conference

PB - Institute of Electrical and Electronics Engineers Inc.

T2 - 2018 Winter Simulation Conference, WSC 2018

Y2 - 9 December 2018 through 12 December 2018

ER -