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The dissertation deals with methods to improve design-based and model-assisted estimation techniques for surveys in a finite population framework. The focus is on the development of the statistical methodology as well as their implementation by means of tailor-made numerical optimization strategies. In that regard, the developed methods aim at computing statistics for several potentially conflicting variables of interest at aggregated and disaggregated levels of the population on the basis of one single survey. The work can be divided into two main research questions, which are briefly explained in the following sections.
First, an optimal multivariate allocation method is developed taking into account several stratification levels. This approach results in a multi-objective optimization problem due to the simultaneous consideration of several variables of interest. In preparation for the numerical solution, several scalarization and standardization techniques are presented, which represent the different preferences of potential users. In addition, it is shown that by solving the problem scalarized with a weighted sum for all combinations of weights, the entire Pareto frontier of the original problem can be generated. By exploiting the special structure of the problem, the scalarized problems can be efficiently solved by a semismooth Newton method. In order to apply this numerical method to other scalarization techniques as well, an alternative approach is suggested, which traces the problem back to the weighted sum case. To address regional estimation quality requirements at multiple stratification levels, the potential use of upper bounds for regional variances is integrated into the method. In addition to restrictions on regional estimates, the method enables the consideration of box-constraints for the stratum-specific sample sizes, allowing minimum and maximum stratum-specific sampling fractions to be defined.
In addition to the allocation method, a generalized calibration method is developed, which is supposed to achieve coherent and efficient estimates at different stratification levels. The developed calibration method takes into account a very large number of benchmarks at different stratification levels, which may be obtained from different sources such as registers, paradata or other surveys using different estimation techniques. In order to incorporate the heterogeneous quality and the multitude of benchmarks, a relaxation of selected benchmarks is proposed. In that regard, predefined tolerances are assigned to problematic benchmarks at low aggregation levels in order to avoid an exact fulfillment. In addition, the generalized calibration method allows the use of box-constraints for the correction weights in order to avoid an extremely high variation of the weights. Furthermore, a variance estimation by means of a rescaling bootstrap is presented.
Both developed methods are analyzed and compared with existing methods in extensive simulation studies on the basis of a realistic synthetic data set of all households in Germany. Due to the similar requirements and objectives, both methods can be successively applied to a single survey in order to combine their efficiency advantages. In addition, both methods can be solved in a time-efficient manner using very comparable optimization approaches. These are based on transformations of the optimality conditions. The dimension of the resulting system of equations is ultimately independent of the dimension of the original problem, which enables the application even for very large problem instances.

The economic growth theory analyses which factors affect economic growth and tries to analyze how it can last. A popular neoclassical growth model is the Ramsey-Cass-Koopmans model, which aims to determine how much of its income a nation or an economy should save in order to maximize its welfare. In this thesis, we present and analyze an extended capital accumulation equation of a spatial version of the Ramsey model, balancing diffusive and agglomerative effects. We model the capital mobility in space via a nonlocal diffusion operator which allows for jumps of the capital stock from one location to an other. Moreover, this operator smooths out heterogeneities in the factor distributions slower, which generated a more realistic behavior of capital flows. In addition to that, we introduce an endogenous productivity-production operator which depends on time and on the capital distribution in space. This operator models the technological progress of the economy. The resulting mathematical model is an optimal control problem under a semilinear parabolic integro-differential equation with initial and volume constraints, which are a nonlocal analog to local boundary conditions, and box-constraints on the state and the control variables. In this thesis, we consider this problem on a bounded and unbounded spatial domain, in both cases with a finite time horizon. We derive existence results of weak solutions for the capital accumulation equations in both settings and we proof the existence of a Ramsey equilibrium in the unbounded case. Moreover, we solve the optimal control problem numerically and discuss the results in the economic context.

This dissertation is dedicated to the analysis of the stabilty of portfolio risk and the impact of European regulation introducing risk based classifications for investment funds.
The first paper examines the relationship between portfolio size and the stability of mutual fund risk measures, presenting evidence for economies of scale in risk management. In a unique sample of 338 fund portfolios we find that the volatility of risk numbers decreases for larger funds. This finding holds for dispersion as well as tail risk measures. Further analyses across asset classes provide evidence for the robustness of the effect for balanced and fixed income portfolios. However, a size effect did not emerge for equity funds, suggesting that equity fund managers simply scale their strategy up as they grow. Analyses conducted on the differences in risk stability between tail risk measures and volatilities reveal that smaller funds show higher discrepancies in that respect. In contrast to the majority of prior studies on the basis of ex-post time series risk numbers, this study contributes to the literature by using ex-ante risk numbers based on the actual assets and de facto portfolio data.
The second paper examines the influence of European legislation regarding risk classification of mutual funds. We conduct analyses on a set of worldwide equity indices and find that a strategy based on the long term volatility as it is imposed by the Synthetic Risk Reward Indicator (SRRI) would lead to substantial variations in exposures ranging from short phases of very high leverage to long periods of under investments that would be required to keep the risk classes. In some cases, funds will be forced to migrate to higher risk classes due to limited means to reduce volatilities after crises events. In other cases they might have to migrate to lower risk classes or increase their leverage to ridiculous amounts. Overall, we find if the SRRI creates a binding mechanism for fund managers, it will create substantial interference with the core investment strategy and may incur substantial deviations from it. Fruthermore due to the forced migrations the SRRI degenerates to a passive indicator.
The third paper examines the impact of this volatility based fund classification on portfolio performance. Using historical data on equity indices we find initially that a strategy based on long term portfolio volatility, as it is imposed by the Synthetic Risk Reward Indicator (SRRI), yields better Sharpe Ratios (SRs) and Buy and Hold Returns (BHRs) for the investment strategies matching the risk classes. Accounting for the Fama-French factors reveals no significant alphas for the vast majority of the strategies. In our simulation study where volatility was modelled through a GJR(1,1) - model we find no significant difference in mean returns, but significantly lower SRs for the volatility based strategies. These results were confirmed in robustness checks using alternative models and timeframes. Overall we present evidence which suggests that neither the higher leverage induced by the SRRI nor the potential protection in downside markets does pay off on a risk adjusted basis.