Mathematische Optimierung und Wirtschaftsmathematik | Mathematical Optimization and Economathematics – serie

Jan Natolski behandelt die Problematik der Quantifizierung des Risikokapitals aus einer theoretischen Perspektive, die in wertvolle Impulse für die praktische Handhabung mündet. Als zentrales Resultat zeigt der Autor, dass die in der Praxis verwendete Methode der Replikation mathematisch fundiert ist.

Manuela Spangler deals with the default risk modelling of German covered bonds (Pfandbriefe). Existing credit risk models are not suitable for this purpose as they only consider the creditworthiness of the issuer while product-specific features are not taken into account. The author develops a multi-period simulation-based Pfandbrief model which adequately accounts for the product’s most important characteristics and risks. The model provides a flexible framework for structural analyses and can be easily extended for tailor-made investigations. While the focus of the work is on the specification of the model itself, simulation results from an exemplary model calibration are also discussed.About the Author Manuela Spangler works as a quantitative risk analyst for a large asset management company and holds a PhD in mathematics from the University of Augsburg. Prior to her current position, she worked as a risk manager and financial engineer in the banking and insurance sector for various years.

Emilia Graß develops a solution method which can provide fast and near-optimal solutions to realistic large-scale two-stage stochastic problems in disaster management. The author proposes a specialized interior-point method to accelerate the standard L-shaped algorithm. She shows that the newly developed solution method solves two realistic large-scale case studies for the hurricane prone Gulf and Atlantic coast faster than the standard L-shaped method and a commercial solver. The accelerated solution method enables relief organizations to employ appropriate preparation measures even in the case of short-term disaster warnings.About the AuthorEmilia Graß holds a PhD from the Hamburg University of Technology, Germany. She is currently working as guest researcher on the project cyber security in healthcare at the Centre for Health Policy, Imperial College London, UK. Her scientific focus is on stochastic programming, solution methods, disaster management and healthcare.

Ole Martin extends well-established techniques for the analysis of high-frequency data based on regular observations to the more general setting of asynchronous and irregular observations.

Oleg Wilfer presents a new conjugate duality concept for geometric and cone constrained optimization problems whose objective functions are a composition of finitely many functions.

Anja Schedel analyzes two models in the field of algorithmic game theory which both constitute bilevel problems in networks. The second model is motivated from privatized public roads, in which private, selfishly acting firms build roads, and as compensation for their investment, are allowed to set prices for using the roads.

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.

In this book Lukas Graf studies dynamic network flows which are a model for individual car traffic in road networks. A dynamic flow wherein every (infinitesimally small) flow particle behaves in this way is then called an instantaneous dynamic equilibrium.