DoCRA - Doctoral Colloquium on Risk Analytics

A joint initiative of Collegio Internazionale Ca’ Foscari Venezia (team leader), IUSS Pavia, IMT Lucca, SISSA Trieste, Scuole di Studi Superiori Carlo Urbani in Camerino, Scuola di Studi Superiori Giacomo Leopardi in Macerata, Scuola Superiore F. Rossi in Torino, Scuola Superiore Universitaria di Toppo Wassermann in Udine

Aims and scope

The Colloquium is an honour course for Doctoral students interested in analytical (both theoretical and applied) methods for the measurement, management and mitigation of risks.

It is organized over four independent 2-week sessions.

Admitted students will be enrolled only if they confirm their interest by sending a non-refundable €120 deposit within five working days from being notified of admission. The deposit mitigates the risk of no-show and will co-fund 10 light lunches during the weekdays.

Target

Students are PhD candidates from Italian or Foreign Universities, who remain affiliated with their Doctoral School.

The maximum size of a class per session is approximately 25.

A group of up to 20 students will be offered up to a maximum of € 200 per person for travel expenses. The organization will book accomodation at identified facilities; the cost will be supported by the organization and therefore will be free for participants. For any information, consult the “Information for students” document. Additional advanced-level students, including further Doctoral Students, Postdocs, Junior Faculty, or PhDs working in the industry, may be admitted at their own expenses.

Practical Information

WHERE

San Servolo Island, Venice

San Servolo is located in Venice’s historic centre, across from Saint Mark’s Square, easily accessible by ACTV public waterbus

WHEN

Four two-weeks sessions between January 2025 and January 2026. The calendar is the following:

1) February, 23 – March, 8, 2025;
2) July, 26 – August, 9, 2025;
3) September, 14 – 27, 2025;
4) January, 18 – 31, 2026.

HOW

Each session offers two courses. Each course is typically delivered over at least 20 hours in one week, combining frontal teaching, office hours/discussions, assignments and presentation of research by the students.

APPLYING

Students can apply for the second session by filling out the form on this page. Deadline: July 13th, 2025. Detailed organizational information will be communicated to the participants.

Who:
The Doctoral Colloquium is organized by the Collegio Internazionale, the Superior School at University Ca’ Foscari Venezia.

Steering Committee:
Elisa Luciano (Chair, U. Torino and Collegio Carlo Alberto), Mavira Mancino (U. Florence).

Executive secretary:
Marco Corazza (U. Ca’ Foscari Venezia)

Advisory Board:
Alessandro Armando (U. Genoa and IMT Lucca), Monica Billio (U. Ca’ Foscari Venezia), Eugenio Coccia (National Commission for the prediction and prevention of major risks), Mariano Croce (U. Bocconi Milano), Giulia Di Nunno (U. Oslo), Marco Frittelli (U. Milano Statale), Mario Martina (IUSS Pavia), Marco Pagano (U. Napoli Federico II), Fabio Trojani (U. Geneva, U. Torino and SFI)

Email:
For information: colloquia.cicf@unive.it

Overview

There are four 2-weeks sessions. A session consists of two consecutive one-week courses, supplemented by one guest lecture on a topic of special interest. Each session can be chosen independently, but each two-week session must be attended in full.

Session 1: Modern risk measurement (23 February–8 March 2025)

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 (Mo 24/2 to Fri 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.

Fri 28/2: GUEST LECTURE on Anatomy and physiology of a cat-risk model

Speaker: Mario Martina, IUSS Pavia

Week 2 (Mo 3/3 to Fri 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 differ- ent 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 sen- sitivity of premiums and solvency capital for NatCat risks under climate change — Theory, concrete calculations, some case studies, exercises.

Session 2: New challenges on long-run risks (27 July–9 August 2025)

NoteStudents 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 (Mo 28/7 to Fri 1/8): MacroFinTech

Lecturer: Max Croce, U. Bocconi

Contents: Modern macrofinance models often take into account the role of news shocks. For news shocks to be priced, preferences should go beyond the expected utility framework. This course has two applied goals. First, familiarize with asset pricing models with recursive preferences in both endowment and production economies. Second, solve macrofinance DSGE models through standard perturbation methods. Becoming knowledgeable about these techniques is extremely beneficial as it increases both the quantity of research papers that can be produced in a short amount of time.

This course is mainly applied, in the sense that we will devote most of our time learning how to solve a model and get results. We will see only a minimum set of theoretical concepts that are essential to check the correctness of the solution and debug our codes. By the end of the course, solving a dynamic stochastic general equilibrium (DSGE) model should be a routine task.

We will work with dynare++.exe, a free stand-alone package that solves stochastic systems of smooth equations. We will also learn how to integrate dynare++.exe with Matlab in order to generate nice tables and figures in an efficient way. We will see recent applications related to:
– MacroFinTech for emissions regulation;
– Supply Chain Uncertainty & Growth;
– Currencies.

Depending on enrollment, some presentations will be assigned to students. We will have 1 or 2 homeworks that will require students to replicate existing papers using dynare++ and Matlab.

Some references:
– Tallarini (2000, JME);
– Bansal and Yaron (2004, JF);
– Kung and Schmit (2013, JF);
– Croce et al (2024), WP, ‘Supply Chain Uncertainty’
– Croce et al (2025), WP, ‘Green Coins’.

Fri 1/8: GUEST LECTURE on Horizon risk, what is it and how to tackle it in a dynamic way

Speaker: Giulia Di Nunno, U. Oslo

Contents: Horizon risk is the assessing the financial exposure by a risk measure that is not adequate to the actual time horizon of the position. We clarify that dynamic risk measures are subject to horizon risk, so we propose to work with fully-dynamic risk measures. We shall combine horizon risk with other uncertainties of the future market scenarios, such as interest rates uncertainty, thus we propose and justify the use of a cash non-additive version. We then construct such risk measures via backward stochastic differential equations or via shortfall-type representation. As illustration, we introduce the class of hq-entropic risk measures.

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

Lecturer: Fabio Trojani, U. Geneva, U. Torino and SFI

Contents: This course covers selected recent research topics in theoretical and empirical asset pricing. The common theme of the lectures is the construction of suitable model-free Stochastic Discount Factors (SDFs) that minimise convenient notions of SDF variability subject to the relevant asset pricing constraints. We cover univariate and multivariate markets, settings with frictions or ambiguity, recoveries based on option price information summarised by suitable portfolios replicating higher moment risk, and further reaching implications for the understanding of asset markets, investors beliefs and asset pricing factors. In parallel, we introduce a systematic convex analysis framework for understanding penalised estimation and inference about minimum dispersion SDFs in presence of pricing errors. Exploiting this estimation and inference approach, we present a new methodology for testing asset pricing models in presence of useless or weak factors. Instead of widely covering several individual approaches and particular directions in the literature, we focus on essential methodologies for applying these techniques with success in a structured and general way.

Reading Material:
1. Own slides
2. Selected research articles

Topics covered:
1. Model-free SDFs and asset pricing bounds
(a) Minimum dispersion SDFs in univariate and multivariate markets
(b) Asset pricing bounds
(c) Implications for international asset pricing
2. Model-free trading of higher-moment risk
(a) Realised measures of higher-moment risk
(b) Replication of higher moment risk
(c) Implied moment surfaces
(d) Implications for the pricing of jump risk
3. Almost model-free SDF recovery
(a) SDF recovery problems
(b) Almost model-free recovery
(c) Implications for conditional SDF modelling
4. Beyond frictionless markets: Smart SDFs
(a) Arbitrage-free pricing with non zero pricing errors
(b) Minimum dispersion Smart SDFs
(c) Relation to APT pricing
(d) Implications for international asset pricing
5. A convex analysis framework for penalised estimation and inference
(a) Basic elements of convex analysis
(b) Penalised estimation and proximal estimation
(b) From regular to singular designs
(c) Inference and Oracle estimation with irregular designs
(d) Insights for asset pricing
6. Tradeable factor risk premia and tests of asset pricing models
(a) Intrinsic factor risk premia
(b) Sample intrinsic factor risk premia
(b) Oracle intrinsic factor risk premium estimation
(c) Intrinsic factor selection and inference with the factor zoo

Students 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).
APPLICATION OPENED

Session 3: AI for Risk (14–27 September 2025)

Week 1 (Mo 15/9 to Tue 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, U. Genoa and IMT Lucca

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

Lecturer: Christa Cuchiero, U. Vienna
APPLICATIONS WILL OPEN SOON

Session 4: Networks and risk propagation (18–31 January 2026)

Week 1 (Mo 19/1 to Fri 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: (Mo 26/1 to Fri 30/1, 2026): Title TBD

Lecturer: Alireza Tahbaz-Salehi, Northwestern University

APPLICATIONS WILL OPEN SOON

Application

How to apply:

1. fill the form in this page within July 13th, 2025
2. one of your faculty member will separately send a reference letter to licalzi@unive.it
3. after we’ll publish the results of the selection on this page, only the selected students have to confirm the participation filling the form that we’ll provide.

INFORMATION FOR STUDENTS

For more information: you can download the Information for students file

Partner

For information:  colloquia.cicf@unive.it

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