Nested Simulations: Theory and Application
1st Edition
Published on 26. March 2024
XVII, 137 pages
978-3-658-43853-1 (ISBN)
Description
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.
More details
Series
Language
English
Place of publication
Wiesbaden
Germany
Publishing group
Springer Fachmedien Wiesbaden GmbH
Target group
Professional and scholarly
Product notice
Reflowable
Illustrations
XVII, 137 p. 18 illus., 17 illus. in color. Textbook for German language market.
File size
2,17 MB
ISBN-13
978-3-658-43853-1 (9783658438531)
DOI
10.1007/978-3-658-43853-1
Schweitzer Classification
Other editions
Additional editions
Maximilian Klein
Nested Simulations: Theory and Application
Book
03/2024
Springer Spektrum
€80.24
Shipment within 10-15 days
Person
Maximilian Klein
holds a PhD in mathematics from the University of Augsburg. Currently, he works as a portfolio manager at an asset management company.
Content
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.
