Nested Simulations: Theory and Application
Maximilian Klein
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Naturwissenschaften, Medizin, Informatik, Technik / Sonstiges
Beschreibung
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.
Kundenbewertungen
Complete Convergence, Moment-based Risk Measures, Convergence Rates, Confidence Intervals, Quantile-based Risk Measures, Almost Sure Convergence, SCR, Solvency II, Nested Monte Carlo Simulation, Life Insurance