Prom./coprom.: Prof.dr.ir. Uzay Kaymak / Prof. João M. Sousa
This work considers the general problem of conditional density estimation, i.e., estimating and predicting the density of a response variable as a function of covariates. The semi-parametric models proposed and developed in this work combine fuzzy and probabilistic representations of uncertainty, while making very few assumptions regarding the functional form of the response variable’s density or changes of the functional form across the space of covariates. These models possess sufficient generalization power to approximate a non-standard density and the ability to describe the underlying process using simple linguistic descriptors despite the complexity and possible non-linearity of this process.
These novel models are applied to real world quantitative finance and risk management problems by analyzing financial time-series data containing non-trivial statistical properties, such as fat tails, asymmetric distributions and changing variation over time.