Reducing Bias in Event Time Simulations via Measure Changes

Kay Giesecke () and Alexander Shkolnik ()
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Kay Giesecke: Department of Management Science and Engineering, Stanford University, Stanford, California 94305
Alexander Shkolnik: Department of Statistics and Applied Probability, University of California, Santa Barbara, California 93106

Mathematics of Operations Research, 2022, vol. 47, issue 2, 969-988

Abstract: Stochastic point process models of event timing are common in many areas, including finance, insurance, and reliability. Monte Carlo simulation is often used to perform computations for these models. The standard sampling algorithm, which is based on a time-change argument, is widely applicable but generates biased simulation estimators. This article develops and analyzes a change of probability measure that can reduce or even eliminate the bias without restricting the scope of the algorithm. A result of independent interest offers new conditions that guarantee the existence of a broad class of point process martingales inducing changes of measure. Numerical results illustrate our approach.

Keywords: Primary: 65C05; 60G55; 60G44; Secondary: 90-10; 91-10; 60J76; simulation bias; point processes; event timing; changes of measure; time scaling; Monte Carlo methods (search for similar items in EconPapers)
Date: 2022
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Persistent link: https://EconPapers.repec.org/RePEc:inm:ormoor:v:47:y:2022:i:2:p:969-988

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