Nested Simulations: Theory and Application

2024
ISBN: 978-3-658-43852-4
Verlag: Springer

Buch, Englisch, 137 Seiten, Format (B × H): 148 mm x 210 mm, Gewicht: 212 g

Reihe: Mathematische Optimierung und Wirtschaftsmathematik | Mathematical Optimization and Economathematics

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.

Zielgruppe

Research

Autoren/Hrsg.

Klein, Maximilian

Fachgebiete

• Mathematik | Informatik Mathematik Mathematik Allgemein
• Mathematik | Informatik Mathematik Numerik und Wissenschaftliches Rechnen Angewandte Mathematik, Mathematische Modelle

Inhaltsverzeichnis

Introduction.- Basic Concepts, Probability Inequalities and Limit Theorems.- Almost Sure Convergence of Moment-Based Estimators.- Almost Sure Convergence of Quantile-Based Estimators.- Non Parametric Confidence Intervals for Quantiles.- Numerical Analysis.- Conclusion.

Über Autor(innen)

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