This chapter presents a comprehensive overview of variance reduction techniques, which are essential for improving the efficiency and accuracy of Monte Carlo simulations. Key methods such as stratified sampling, antithetic variates, common random numbers, control variates, conditional Monte Carlo, and importance sampling are explained and illustrated with practical examples. Special attention is given to the cross-entropy method and its applications in rare event simulation. The chapter discusses the theoretical motivation behind each technique, their implementation in Python, and the impact on estimator variance and computational cost. Applications in fields such as finance and actuarial science are highlighted, demonstrating the practical benefits of variance reduction in real-world problems. Throughout, readers are provided with step-by-step algorithms, illustrative figures and tables, and publicly available Python code, enabling them to implement and compare variance reduction methods in their own simulation studies.

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Variance Reduction Techniques

  • Paweł Lorek,
  • Tomasz Rolski

摘要

This chapter presents a comprehensive overview of variance reduction techniques, which are essential for improving the efficiency and accuracy of Monte Carlo simulations. Key methods such as stratified sampling, antithetic variates, common random numbers, control variates, conditional Monte Carlo, and importance sampling are explained and illustrated with practical examples. Special attention is given to the cross-entropy method and its applications in rare event simulation. The chapter discusses the theoretical motivation behind each technique, their implementation in Python, and the impact on estimator variance and computational cost. Applications in fields such as finance and actuarial science are highlighted, demonstrating the practical benefits of variance reduction in real-world problems. Throughout, readers are provided with step-by-step algorithms, illustrative figures and tables, and publicly available Python code, enabling them to implement and compare variance reduction methods in their own simulation studies.