Simulation of multidimensional diffusions with sticky boundaries via Markov chain approximation

Christian Meier, Lingfei Li and Gongqiu Zhang

European Journal of Operational Research, 2023, vol. 305, issue 3, 1292-1308

Abstract: In this study, we develop a novel method to simulate multidimensional diffusions with sticky boundaries for which the Euler scheme fails. We approximate the sticky diffusion process by a multidimensional continuous-time Markov chain (CTMC) that can be easily simulated. We provide two approaches to construct the CTMC. In the first approach, we approximate the infinitesimal generator of the sticky diffusion by finite difference using standard coordinate directions. In the second one, we match the local moments using the drift and the eigenvectors of the covariance matrix as transition directions. The first approach does not always guarantee a valid Markov chain, whereas the second one can. We show that both construction methods yield a first-order simulation scheme, which can capture the sticky behavior and is free from the curse of dimensionality. As applications, we use our method to simulate the limit of a queuing system with exceptional service policy and a multi-factor short rate model for low interest rate environment.

Keywords: Applied probability; Multidimensional diffusions; Sticky boundary; Markov chain approximation; Monte Carlo simulation (search for similar items in EconPapers)
Date: 2023
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Citations: View citations in EconPapers (3)

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Persistent link: https://EconPapers.repec.org/RePEc:eee:ejores:v:305:y:2023:i:3:p:1292-1308

DOI: 10.1016/j.ejor.2022.07.038

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