My teaching focuses on probability, statistics and stochastic modelling, with particular emphasis on actuarial applications and the quantitative analysis of risk.
The courses presented here combine mathematical foundations, statistical methodology and applications. They are designed to develop both a rigorous understanding of the underlying models and the ability to use them on real-world problems in insurance, finance and risk management.
Course notes and video lectures are available for the three main courses below.
How can an insurer quantify and manage the risk of future losses?
Risk theory provides the probabilistic foundations for modelling the risks faced by insurance companies. It addresses fundamental actuarial questions: how should a random risk be priced? How can the aggregate loss of an insurance portfolio be modelled? How can the probability of ruin be quantified, and how do large claims affect the solvency of an insurer?
The course covers premium principles and risk measures, individual and collective risk models, aggregate claims distributions, the Cramér–Lundberg model and classical ruin theory. Particular attention is also paid to reinsurance mechanisms and to the distinction between light-tailed and heavy-tailed risks.
The emphasis throughout the course is on connecting probabilistic models with actuarial decision-making.
How can we estimate an event that has never yet been observed?
Extreme Value Theory provides a probabilistic and statistical framework for analysing rare events occurring in the tails of distributions. Such events include very large insurance claims, natural catastrophes, extreme environmental measurements and severe financial losses.
The course begins with the asymptotic theory of maxima, GEV distributions and domains of attraction, before introducing threshold exceedances, Generalized Pareto distributions and point-process representations. Statistical inference for extremes is then developed, including tail-index estimation, extreme quantiles and return levels.
The second part of the course extends these ideas to dependent and multivariate extremes, with topics including the extremal index, clustering of extremes, multivariate max-stable distributions, copulas and tail dependence.
How much can the past tell us about the future?
Time series analysis studies phenomena observed sequentially through time, where the ordering and dependence of observations contain essential information. The objective is to identify temporal structures, construct stochastic models for their dynamics and use these models for forecasting.
The course starts with trend, seasonality and stationarity, together with decomposition and filtering methods. It then develops the theory of stationary and linear processes, autocorrelation and partial autocorrelation, spectral analysis and the Wold representation.
A central part of the course is devoted to ARMA, ARIMA and SARIMA models, their identification, estimation and validation within the Box–Jenkins methodology. The final chapters address forecasting and ARCH/GARCH models for time-varying volatility, with extensive applications and implementations in R.
Each course is accompanied by detailed lecture notes, examples and exercises. Video lectures provide a complementary presentation of the main concepts and can be used either alongside the written material or for independent review.