Topics for master's theses

An important application area of logistic regression is credit scoring. In credit scoring, the task is to build a model  which can predict the probability that  a loan applicant is good i.e. will pay back the loan. As a rule, many of the independent variables used in modelling are nominal or discrete (gender, family status, education, etc). A usual way to handle nominal predictors is to introduce dummy (1-0) variables for each of k categories of the initial nominal variable. As an alternative, weight of evidence (WOE) coding  is used to prepare a nominal predictor for usage in binary logistic regression models by transforming it into one single numerical variable. In this work, the student will have a real data set to analyze and build a credit scoring system by using WOE methodology. The results obtained will be compared with traditional logistic regression based on dummy variables.

In the master's thesis, it is planned to look at various multi-asset options and the methods proposed in the literature for their pricing. Multi-asset options include, for example, rainbow options, in which the payoff depends on the maximum (or minimum) price of n assets at expiry and basket options, where the payoff depends on the weighted price of n assets. For pricing such options special types of binomial lattice methods or Monte-Carlo methods are used. It is planned to draw up the corresponding programs and carry out numerical experiments.

In simple terms, two non-stationary time series are cointegrated if there is such a linear combination of these time series that is a stationary time series. For example, exchange rates or prices of different energy carriers behave according to a random walk process (being therefore non-stationary), but in the case of cointegration, the behavior of these time series is consistent with each other in the long run. If  two time series are cointegrated, we can present the so-called long-term and short-term relationship of these time series in the form of an error correction model. In the Master's thesis, it is planned to give a theoretical overview of the cointegration of time series, and in the practical part of the work, to study the cointegration of exchange rates or the price of different energy carriers. 

k Nearest Neighbors method is a well-known method which can be used for solving both regression and classification problems. Although it is based on a very simple idea, there are several aspects of the method which are usually not covered in main textbooks and courses about machine learning. The aim of the thesis is to develop a comprehensive overview of different aspects of the method and it's modifications together with illustrating numerical examples. The text of the thesis should be suitable for supplementary study material for machine learning course.

In order to complete the thesis, it is necessary to present clearly mathematical background of various ideas and to implement some non-standard versions of Nearest Neighbors method in Python or in R.

In the life-insurance business it is essential for the company to estimate the life expectancy of a client. In non-life insurance and in other financial enterprises it is often of interest to evaluate the loyalty of a client, for example, via the duration of the contract. Life expectancy and duration of the contract are typically influenced by many factors, and it is very important to find possible associations in order to account for them during the price development, prevention or even choosing potential clients. One way is to use only historic data but, in that case, we are omitting data of those clients who are currently alive/existing in our client base. The latter issue brings us to censoring and to overcome this issue pseudo-observations have been proposed. Student will focus on pseudo-observation use cases for restricted mean survival time and possibly competing risk type of scenarios depending on data availability. 

Portfolio reinsurance is a type of insurance transaction involving two or more insurance companies.
The purchaser of portfolio reinsurance provides the reinsurer with the insurance premiums received from the policies being reinsured. In exchange, the reinsurer assumes the risk for any future claims associated with those policies.
During the implementation of the thesis various methods of optimisation of this mechanism will be considered.
A simulation model will be developed to study the link between risks and reinsurance parameters.