Consistency in portfolio optimization : a new approach using the general framework of portfolio theory

Brenner, René; Maier-Paape, Stanislaus (Thesis advisor); Zhu, Qiji Jim (Thesis advisor)

Aachen : RWTH Aachen University (2021, 2022)
Dissertation / PhD Thesis

Dissertation, RWTH Aachen University, 2021

Abstract

In line with the general framework of portfolio optimization this thesis shows strong consistency of portfolio optimization problems with constrained utility for lower semi-continuous convex (extended) risk and upper semi-continuous concave (extended) utility functions. It also shows measurability of solutions of the empirical optimization problem. Numerical results are presented showing the empirical efficient frontier, i.e. the empirical risk andutility values of numerical solutions to different utility lower bounds µ, for the so called empiricallog-drawdown risk setup. Furthermore, a statistical analysis of consistency of empirical solutions isgiven. These evaluations are done based on real historical market data with the software environment POEM which was designed especially for backtesting portfolio optimizations.