DoCRA project 
Doctoral Colloquium on Risk Analytics

Note: Students admitted to this session must have a knowledge of probability theory that includes at least what is treated in chapters 1-4 in Olofsson and Andersson, "Probability, Statistics, and Stochastic Processes", 2nd edition, 2012.

Week 1 (Monday 24/2 to Friday 28/2):
Measuring and comparing risks

• Lecturer: Alfred Muller, U. Siegen
• Contents: We cover modern mathematical methods for measuring and comparing risks, motivated by properties that are desirable in applications. We start with the comparison of risks, leading to the mathematical notion of order relations for probability measures (also known as stochastic orders). We discuss these concepts in detail, give an overview of recent research on their generalizations, and examine their robustness. We move on to the comparison of multivariate risks, where the dependence structure also plays a role. We discuss in particular the supermodular stochastic order to compare dependence structures, which includes the study of copulas and comonotonicity. We also consider the general relation between stochastic orders and the modern topic of optimal transport, which is a relatively new field of research.
• The second main topic are measures of risk that play an important role in actuarial or financial risks, in the form of premium principles or of regulatory capital requirements. We follow an axiomatic approach and discuss mathematical properties of such risk measures like coherence, convexity and elicitability. We discuss the properties of well-known examples including value-at-risk, conditional value at risk, expectiles, certainty equivalents, as well as principles based on mean and variance.

Guest Lecture (Friday 28/2):
Anatomy and physiology of a cat-risk model

• Speaker: Mario Martina, IUSS Pavia

Week 2 (Monday 3/3 to Friday 7/3):
Emerging risks for actuaries: NatCat insurance and climate change

• Lecturer: Hansjörg Albrecher, U. Lausanne
• Contents: Insurance of natural catastrophies: what is specific about it, what makes it different from other insurance sectors (premiums, capital) — Analysis of very heavy tails (some extreme value analysis, insurability when only finitely many moments exist) — Dependence models in this context — Quantify the pooling potential (diversification benefit in space and in time) — Assess the degree of climate change (a little flavor of time series analysis, non-stationarities, change points versus trend analysis) — Quantitative effects on the sensitivity of premiums and solvency capital for NatCat risks under climate change — Theory, concrete calculations, some case studies, exercises.

Note: Students admitted to this session must have basic knowledge in theoretical and empirical asset pricing (e.g., see topics reported in the J Chocrane book, "Asset Pricing"); financial econometrics (multivariate linear regressions; time-series econometrics; forecasting; GMM; GARCH; estimation of APT models).

Week 1 (Monday28/7 to Friday 1/8):
MacroFinTech

• Lecturer: Max Croce, U. Bocconi

Guest Lecture: TBA

• Speaker: TBC

Week 2 (Monday 4/8 to Friday 8/8):
Model free pricing and estimation of financial risks

• Lecturer: Fabio Trojani, SFI and U. Torino

Week 1 (Monday 15/9 to Tuesday 23/9):
Predictive uncertainty in Machine Learning with conformal inference

• Lecturer: Stefano Favaro, U. Torino and Collegio Carlo Alberto

Guest Lecture:
Introduction to CyberRisk

• Speaker: Alessandro Armando, IMT Lucca

Week 2 (Monday 21/9 to Friday 25/9):
Concepts of Deep Learning and applications to Finance and Risk Management

• Lecturer: Christa Cuchiero, U. Vienna

Week 1 (Monday 19/1 to Friday 23/1, 2026): Title TBD

• Lecturer: Remco Hofstad, Eindhoven U. of Technology

Guest Lecture:
Title TBD

• Speaker: Monica Billio, U. Ca’ Foscari Venezia

Week 2: (Monday 26/1 to Friday 30/1, 2026): Title TBD

• Lecturer: Alireza Tahbaz-Salehi, Northwestern University