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Stratified Monte Carlo simulation of Markov chains

Author

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  • Fakhereddine, Rana
  • Haddad, Rami El
  • Lécot, Christian
  • Maalouf, Joseph El

Abstract

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 N 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.

Suggested Citation

  • Fakhereddine, Rana & Haddad, Rami El & Lécot, Christian & Maalouf, Joseph El, 2017. "Stratified Monte Carlo simulation of Markov chains," Mathematics and Computers in Simulation (MATCOM), Elsevier, vol. 135(C), pages 51-62.
    • Handle: RePEc:eee:matcom:v:135:y:2017:i:c:p:51-62
    DOI: 10.1016/j.matcom.2016.12.004
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    References listed on IDEAS

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    1. El Haddad, R. & Lécot, C. & L’Ecuyer, P. & Nassif, N., 2010. "Quasi-Monte Carlo methods for Markov chains with continuous multi-dimensional state space," Mathematics and Computers in Simulation (MATCOM), Elsevier, vol. 81(3), pages 560-567.
    2. Evans, Michael & Swartz, Timothy, 2000. "Approximating Integrals via Monte Carlo and Deterministic Methods," OUP Catalogue, Oxford University Press, number 9780198502784, Decembrie.
    3. Russell C. H. Cheng & Teresa Davenport, 1989. "The Problem of Dimensionality in Stratified Sampling," Management Science, INFORMS, vol. 35(11), pages 1278-1296, November.
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