Nested Simulations: Theory and Application
Seiten
2024
|
2024
Springer Fachmedien Wiesbaden GmbH (Verlag)
978-3-658-43852-4 (ISBN)
Springer Fachmedien Wiesbaden GmbH (Verlag)
978-3-658-43852-4 (ISBN)
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.
Maximilian Klein holds a PhD in mathematics from the University of Augsburg. Currently, he works as a portfolio manager at an asset management company.
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.
| Erscheinungsdatum | 28.03.2024 |
|---|---|
| Reihe/Serie | Mathematische Optimierung und Wirtschaftsmathematik |
| Zusatzinfo | XVII, 137 p. 18 illus., 17 illus. in color. Textbook for German language market. |
| Verlagsort | Wiesbaden |
| Sprache | englisch |
| Maße | 148 x 210 mm |
| Themenwelt | Mathematik / Informatik ► Mathematik |
| Schlagworte | almost sure convergence • Complete Convergence • confidence intervals • convergence rates • life insurance • Moment-based Risk Measures • Nested Monte Carlo Simulation • Quantile-based Risk Measures • SCR • Solvency II |
| ISBN-10 | 3-658-43852-5 / 3658438525 |
| ISBN-13 | 978-3-658-43852-4 / 9783658438524 |
| Zustand | Neuware |
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