Stratified Monte Carlo simulation of Markov chains

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• 作者：Rana Fakhereddine^a ; ^{ranafakhreddine@hotmail.com} ; Rami El Haddad^a ; ^{rami.haddad@usj.edu.lb} ; Christian Lé ; cot^b ; ^{christian.lecot@univ-smb.fr} ; Joseph El Maalouf^a ; ^{joseph.maalouf1@net.usj.edu.lb}
• 关键词：Stratified sampling ; Monte Carlo simulation ; Markov chains
• 刊名：Mathematics and Computers in Simulation
• 出版年：2017
• 出版时间：May 2017
• 年：2017
• 卷：135
• 期：Complete
• 页码：51-62
• 全文大小：291 K
• 卷排序：135

文摘

We present several Monte Carlo strategies for simulating discrete-time Markov chains with continuous multi-dimensional state space; we focus on stratified techniques. We first analyze the variance of the calculation of the measure of a domain included in the unit hypercube, when stratified samples are used. We then show that each step of the simulation of a Markov chain can be reduced to the numerical integration of the indicator function of a subdomain of the unit hypercube. Our approach for Markov chains simulates NN copies of the chain in parallel using stratified sampling and the copies are sorted after each step, according to their successive coordinates. We analyze variance reduction on examples of pricing of European and Asian options: enhanced efficiency of stratified strategies is shown.