Winner of the GAUSS Price for Young Academics 2020

The doctoral thesis which is presented here in this short talk studies stochastic portfolio optimization problems with finite horizon in a complete continuous-time financial market model that consists of multiple asset classes, where a pension fund investor desires to maximize her expected utility assigned to the terminal wealth and the intertemporal consumption/pension or buffer rate. We consider various model extensions to traditional approaches such as a more realistic behavioral model for the investor’s risk preferences, age-dependent risk aversion and the involvement of buffer mechanisms and pension adjustment rules in the absence of guarantees. Moreover, economic interpretations and justifications of the proposed models are provided. The associated portfolio selection problems are solved by applying case-specific optimization methodologies; in particular we employ the Martingale method and Merton’s approach, combined with suitable transformations of the optimization problems. The solutions in form of optimal quantitative dynamic asset allocation and consumption strategies as well as corresponding optimal replicating wealth processes are achieved for the flexible class of hyperbolic absolute risk aversion (HARA) utility functions. The relevance of the proposed models is illustrated in numerical optimization and simulation case studies which are carried out to elaborate on the characteristics and impact of the determined optimal investment strategies.