Topics for master's theses 2025/2026

Description: The classical Cramér–Lundberg model is one of the foundational frameworks in actuarial risk theory, used to describe the surplus of an insurance company over time. While much is known about the asymptotic ruin probabilities under idealized conditions, less attention has been paid to the stability of these approximations under model perturbations — such as discretized (quantized) claims, parameter uncertainty, or approximation of claim size distributions. This thesis investigates how sensitive the Cramér–Lundberg ruin probability and the associated Lundberg adjustment coefficient are to such approximations. The student will explore both analytical results (e.g., convergence of moment generating functions and adjustment coefficients) and simulation-based validation.

Possible directions:

· Study the convergence of the Lundberg exponent under discretized or quantized claim distributions.

· Examine the effect of claim size truncation or rounding on the accuracy of the ruin probability approximation.

· Explore numerical or simulation-based methods to assess stability in practical applications.

Recommended background: Probability theory, stochastic processes, and basic knowledge of insurance mathematics or applied statistics.

Key references:

1. Rolski, T., Schmidli, H., Schmidt, V., & Teugels, J. L. (1999). Stochastic Processes for Insurance and Finance. Wiley.

2. Asmussen, S., & Albrecher, H. (2010). Ruin Probabilities (2nd ed.). World Scientific.

3. Albrecher, H., & Kortschak, D. (2009). “On the Adjustment Coefficient, the Lundberg Equation and Related Topics.” Insurance: Mathematics and Economics, 44(1), 20–26.

Description: Credit scoring models are central to modern risk management and regulatory frameworks such as Basel III. The goal of this thesis is to study the full lifecycle of a credit risk scoring model — from data preprocessing and feature engineering to model development, validation, and interpretation. The student will work with real or simulated loan-level data to develop a Probability of Default (PD) model using methods such as logistic regression, survival analysis, or machine learning. Emphasis will be placed on model stability, fairness, and interpretability — ensuring that the scoring model is both predictive and transparent for business decision-making.

Possible directions:

· Compare traditional logistic regression models with machine learning approaches (e.g., gradient boosting, random forests).

· Develop and validate a Lifetime PD model based on survival analysis techniques.

· Investigate feature stability and model performance over time and across customer segments.

Recommended background: Applied statistics, econometrics, or data science; familiarity with statistical software (Python, R, or SQL).

Key references:

1. Thomas, L. C. (2009). Consumer Credit Models: Pricing, Profit, and Portfolios. Oxford University Press.

2. Siddiqi, N. (2017). Intelligent Credit Scoring: Building and Implementing Better Credit Risk Scorecards (2nd ed.). Wiley.

3. Bellotti, T., & Crook, J. (2009). “Credit Scoring with Macroeconomic Variables Using Survival Analysis.” Journal of the Operational Research Society, 60(12), 1699–1707.