Robustní optimalizace portfolia

V predloženej práci študujeme optimalizáciu portfólia v podmienkach ce- ločíselnosti, ktoré ovplyvňujú optimálnu alokáciu aktív. Zadefinujeme miery rizika a formulujeme "mean-risk" modely. K vytvoreniu robustných modelov zahrňujúcich neurčitosť v pravdepodobnostnom rozdelení použijeme dve metódy: analýza najhor- šieho prípadu a kontaminácia. Neurčitosť v diskrétnom pravdepodobnostnom rozde- lení uvažujeme v hodnotách scenárov a v ich pravdepodobnostiach najprv samostatne a následne v kombinácii. Vytvorené modely sú aplikované na dáta z akciového trhu pomocou optimalizačného softvéru GAMS.In this thesis, a portfolio optimization with integer variables which influ- ence optimal assets allocation, is studied. Measures of risk are defined and the cor- responding mean-risk models are derived. Two methods are used to develop robust models involving uncertainty in probability distribution: the worst-case analyses and contamination. The uncertainty in values of scenarios and in their probabili- ties of the discrete probability distribution is assumed separately followed by their combination. These models are applied to stock market data with using optimization software GAMS.Department of Probability and Mathematical StatisticsKatedra pravděpodobnosti a matematické statistikyFaculty of Mathematics and PhysicsMatematicko-fyzikální fakult

Robust portfolio selection problem

In this thesis, a portfolio optimization with integer variables which influ- ence optimal assets allocation, is studied. Measures of risk are defined and the cor- responding mean-risk models are derived. Two methods are used to develop robust models involving uncertainty in probability distribution: the worst-case analyses and contamination. The uncertainty in values of scenarios and in their probabili- ties of the discrete probability distribution is assumed separately followed by their combination. These models are applied to stock market data with using optimization software GAMS

Robust portfolio selection problem

In this thesis, a portfolio optimization with integer variables which influ- ence optimal assets allocation, is studied. Measures of risk are defined and the cor- responding mean-risk models are derived. Two methods are used to develop robust models involving uncertainty in probability distribution: the worst-case analyses and contamination. The uncertainty in values of scenarios and in their probabili- ties of the discrete probability distribution is assumed separately followed by their combination. These models are applied to stock market data with using optimization software GAMS

Combinatorial portfolio optimization

In this thesis, a portfolio optimization with integer variables which influence optimal assets allocation, is studied. At the beginning basic terms, measures of risk - variance, Value at Risk (VaR), Conditional Value at Risk (CVaR) are defined and the mean-risk models are derived for a practical application. Heuristics and standard algorithms of software GAMS are used for solving problems of the combinatorial portfolio optimization. Two types of the he- uristics are described: the Threshold Acceptance and the Genetic Algorithm. The heuristics are implemented in the MATLAB, applied on financial data and compared with an output of the software GAMS.