PhD Defence: Conditional Density Models Integrating Fuzzy and Probabilistic Representations of Uncertainty

Making decisions based on risk forecasts is an integral part of financial markets’ operations. However, current methods of defining risk are not always sufficiently informative. In his PhD dissertation entitled ‘<link doctoral-programme phd-in-management phd-projects detail>Conditional Density Models Integrating Fuzzy and Probabilistic Representations of Uncertainty’, Rui Jorge Almeida develops new risk models that allow the definition of risk in non-precise linguistic terms that make forecasts more informative.

Humans constantly make risk assessments in diverse situations based on available information, and they often adjust their behaviour accordingly. If the morning forecast indicates a 0% chance of rain, most people will not take an umbrella. If there is a 100% chance of rain, most people will. Any value in between, which incidentally is where the majority of decisions are made, and personal preferences or costs will dictate the call. Similarly, investors and policy makers are interested not only in one single value for the return forecast but also in the risk or possibility that this forecast may differ from the expected value, especially under the worst case scenario.

Financial markets have a complex and volatile nature, making risk management an important activity for financial institutions that operate in these markets. A key aspect of risk management is risk assessment which involves the determination of the risks associated with a business or investment. As a result of risk management, activities are undertaken to reduce the possibility of failure to an acceptable range. Nowadays, the financial sector operates under strict guidelines, which have been imposed through international agreements to manage the different kinds of risks that they are exposed to. Due to the complex nature of financial markets, in which many parties exchange information and interact through trading, the overall risk for a company is influenced by many internal and external factors. There is a need for a concise representation of the risk a company or institution is facing to keep the risk management problem tractable. This summarization of risk can be based on the worst expected loss for a given horizon and translated into easily understandable categories by credit rating agencies.

The models developed in this thesis combine the concepts of risk and linguistic descriptors which naturally reflect in-between values and category summarizations. The combination of these concepts results in flexible and accurate models, containing imprecise descriptions of phenomena – similar to common human descriptions. These models also have the advantages that they can be used to describe process knowledge in the form of rules without very strict assumptions – which is very natural for humans – and allow economic decision makers to understand and perform adequate risk management.

Rui Jorge Almeida defended his dissertation in the Senate Hall at Erasmus University Rotterdam on Thursday, 26 June 2014. His supervisors were Professor Uzay Kaymak (Technische Universiteit Eindhoven) and  Professor João Sousa (Universidade de Lisboa). Other members of the Doctoral Committee were <link people patrick-groenen>Professor Patrick Groenen and <link people jaap-spronk>Professor Jaap Spronk (ERIM), and Professor Trevor Martin (University of Bristol).

About Rui Jorge Almeida

Rui Jorge Almeida graduated from a five year program (licentiate) in Mechanical Engineering (2005) and received his MSc in Mechanical Engineering (2006), both titles obtained from Instituto Superior Técnico, Technical University of Lisbon. He is currently a PhD Candidate at the Department of Econometrics of the Erasmus School of Economics, Erasmus University Rotterdam. His research interests include fuzzy decision making, combining fuzzy modelling techniques and statistical methods as well as data mining in finance

Abstract of Conditional Density Models Integrating Fuzzy and Probabilistic Representations of Uncertainty

Conditional density estimation is an important problem in a variety of areas such as system identification, machine learning, artificial intelligence, empirical economics, macroeconomic analysis, quantitative finance and risk management.

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 analysing financial time-series data containing non-trivial statistical properties, such as fat tails, asymmetric distributions and changing variation over time.

Photos: Chris Gorzeman / Capital Images