Nested Simulations: Theory and Application / by Maximilian Klein

By:

Klein, Maximilian [VerfasserIn]

Resource type: Ressourcentyp: Buch (Online)Book (Online)Language: English Series: Mathematische Optimierung und Wirtschaftsmathematik / Mathematical Optimization and EconomathematicsPublisher: Wiesbaden : Springer Fachmedien Wiesbaden, 2024Publisher: Wiesbaden : Imprint: Springer Spektrum, 2024Edition: 1st ed. 2024Description: 1 Online-Ressource(XVII, 137 p. 18 illus., 17 illus. in color. Textbook for German language market.)ISBN:

9783658438531

Subject(s):

Mathematics

Additional physical formats: 9783658438524 | 9783658438548 | Erscheint auch als: 9783658438524 Druck-Ausgabe | Erscheint auch als: 9783658438548 Druck-Ausgabe | Erscheint auch als: Nested simulations: theory and application. Druck-Ausgabe Wiesbaden : Springer Fachmedien Wiesbaden GmbH, 2024. xvii, 137 SeitenDOI: DOI: 10.1007/978-3-658-43853-1Online resources:

Summary: 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.Summary: 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. 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.PPN: PPN: 1884809146Package identifier: Produktsigel: ZDB-2-SEB | ZDB-2-SNA

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