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Nested Simulations: Theory and Application

  • Book
  • © 2024

Overview

Authors:
  1. Maximilian Klein

    1. Institute of Mathematics, University of Augsburg, Augsburg, Germany

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Table of contents (7 chapters)

  1. Front Matter

    Pages i-xvii
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  2. Introduction

    • Maximilian Klein
    Pages 1-35

  3. Basic Concepts, Probability Inequalities and Limit Theorems

    • Maximilian Klein
    Pages 37-44

  4. Almost Sure Convergence of Moment-Based Estimators

    • Maximilian Klein
    Pages 45-68

  5. Almost Sure Convergence of Quantile-Based Estimators

    • Maximilian Klein
    Pages 69-87

  6. Non Parametric Confidence Intervals for Quantiles

    • Maximilian Klein
    Pages 89-101

  7. Numerical Analysis

    • Maximilian Klein
    Pages 103-122

  8. Conclusion

    • Maximilian Klein
    Pages 123-126

  9. Back Matter

    Pages 127-137
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Keywords

About this book

Maximilian Klein analyses nested Monte Carlo simulations for the approximation of conditional expected values. Thereby, the book deals with two general risk functional classes for conditional expected values, on the one hand the class of moment-based estimators (notable examples are the probability of a large loss or the lower partial moments) and on the other hand the class of quantile-based estimators. For both functional classes, the almost sure convergence of the respective estimator is proven and the underlying convergence speed is quantified. In particular, the class of quantile-based estimators has important practical consequences especially for life insurance companies since the Value-at-Risk falls into this class and thus covers the solvency capital requirement problem. Furthermore, a novel non parametric confidence interval method for quantiles is presented which takes the additional noise of the inner simulation into account.

Authors and Affiliations

  • Institute of Mathematics, University of Augsburg, Augsburg, Germany

    Maximilian Klein

About the author

 Maximilian Klein holds a PhD in mathematics from the University of Augsburg. Currently, he works as a portfolio manager at an asset management company.

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