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.

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).

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’.

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.

The prerequisites for the first week of classes are covered in: Wasserman L. (2013). All of Statistics: A Concise Course in Statistical Inference. Springer Texts in Statistics – all chapters except 16, 17 and 18.
The background required for the first week of classes includes:

• Basic mathematics (linear algebra, and analysis);
• Basic probability theory, as, e.g., in: Jacod J., Protter P. (2004). Probability Essentials. Springer;
• Basics of mathematical finance and stochastic analysis, as, e.g., in: Shreve S.E. (2004). Stochastic Calculus for Finance I and II. Springer.

Conformal prediction (a.k.a conformal inference) offers a powerful framework to construct distribution-free prediction sets for machine learning algorithms.
The goal of this short course is to provide students with the theoretical underpinnings of conformal prediction: Uncertainty quantification for prediction – How does conformal prediction work? – Data exchangeability and related properties – Conformal prediction and marginal non-asymptotic guarantees – Conditional non-asymptotic guarantees – Conformal prediction for classification and its asymptotic (optimality) guarantees – Conformal prediction for regression and its asymptotic (optimality) guarantees – Online conformal prediction for streaming data.
Depending on student’ interest and time available, extra topics on conformal prediction will be assigned as readings (e.g., conformal prediction in small summaries of big data; conformal Bayesian computation; conformal classification with unknown label spaces; conformal prediction in algorithmic fairness).

Core themes of the course are concepts of deep learning (DL), reinforcement learning (RL) as well as generative artificial intelligence (GenAI). This is then complemented by applications in Finance and Risk Management.
The course will cover in particular foundations of deep learning, ranging from different types of deep artificial neural networks to learning and training concepts like stochastic gradient descent methods. Additionally we will also focus on dynamical deep learning approaches like signature methods for time-series data.
For reinforcement learning we shall introduce the concept of Markov decision processes, the Bellman optimality equations and several algorithms like variants of deep Q-learning.
In view of of generative AI we shall mainly focus on transformer and self attention
methodology applied in large language models.
In terms of applications the focus lies on deep hedging, deep portfolio selection, market generators and prediction methodologies.

The background required for the first week of classes includes basic training in first-year economics (e.g., general equilibrium, firm optimization, consumer optimization), some knowledge of linear algebra (e.g., eigenvalues, matrix inversion, solving linear systems of equations) and basic analysis (e.g., Taylor expansions), basic measure theory and probability, including random variables and processes, and Markov processes.
This second week of classes is aimed at students who are familiar with basic ideas in
economic theory (e.g., Nash equilibria and competitive markets) at the level of first-year graduate courses in economics. The course requires familiarity with standard concepts in linear algebra, probability theory, and optimization. Beyond those concepts, the course will be self-contained. No prior knowledge of graph theory is necessary. While some of the applications are inspired by topics in macroeconomics, no prior courses in macroeconomic courses are necessary.

The content of the first week of classes will mainly make use of selected material from various sources. The main source will be the books:

• Remco van der Hofstad: Random Graphs and Complex Networks, Vol. 1. Cambridge University Press, 2016
• Remco van der Hofstad: Random Graphs and Complex Networks, Vol. 2. Cambridge University Press, 2016
• Remco van der Hofstad: Stochastic Processes on Random Graphs. Lecture Notes for the 47th Summer School in Probability Saint-Flour 2017

The first week of classes will treat the following material:

Real-world networks

• Graphs, their degrees and connectivity structure
• Sparse and scale-free degree sequences
  • Highly-connected graph sequences
  • Small-world random graph sequences
  • Further network statistics
  • Null models and network science

Random graphs as models for real-world networks
More realistic random graph models:

• Rank-1 inhomogeneous random graphs
  • Weight conditions Degrees GRG conditioned on degrees is uniform
• Configuration model
  • Construction and law graph
  • Conditions on degrees
  • Degrees erased CM conditioned on simplicity
  • Relation to uniform simple graphs and GRG
• Preferential Attachment Models

Structural properties of random graphs

• Branching processes
• Connectivity structure CM
  • Giant component for CM
  • Connectivity of CM

Branching process comparisons

• Branching process comparisons for random graphs
• Comparison of neighborhoods
• Small-world properties and relations to branching processes

Dense versus sparse models (very brief)

• Intro to dense random graphs
• How sparse or dense are real-world networks?
• Graphons
• Exponential random graphs

Community structures

• Networks and their community structure
• Light intro to community detection
• Stochastic block model, Hierarchical configuration model

Local convergence of random graphs

• Intro to local convergence (LC)
• Local convergence for random graphs
  • LC for the CM
  • Brief discussion of LC for related models
  • Brief application

Information diffusion on networks

• Smallest-weight routing on random graphs
• Markovian setting
• CTBPs and their use in smallest-weight routing on random graphs
• Explosion of smallest-weight routing in scale-free random graphs
• Models for competition on networks and marketing: The winner takes it all
• It is hard to kill fake news

Network vulnerability and percolation

• Attack vulnerability: Directed attack, Random attack and percolation
• Phase transition on CM using Janson’s construction
• Possibly: Bootstrap percolation and avalanches in networks
• Brief overview: critical behavior percolation on random graphs

Statistics for dynamical networks

• Estimation for preferential attachment models: Estimation of the attachment function
• Estimation in the superstar model
• Change-point detection in preferential attachment models
• Network models for citation networks: Citation networks and their structure
• Random graph models for citation networks

Network statistics and centrality measures

• Degree-degree dependencies
• Degree centrality, PageRank, closeness and betweenness centrality and their relations
• Local convergence of centrality measures: When does this hold and when not?

The assessment for the course will be based on exercises to be solved during the course itself.

Multidimensional arrays (i.e. tensors) of data are becoming increasingly available and call for suitable econometric tools. Approaches are first revised for extraction of the network also discussing the importance of topology and structure of the data. A new dynamic linear regression model is then proposed for tensor-valued response variables and covariates that encompasses some well-known multivariate models such as SUR, VAR, VECM, panel VAR and matrix regression models as special cases. For dealing with the over-parametrization and over-fitting issues due to the curse of dimensionality, a suitable parametrization is exploited based on the parallel factor (PARAFAC) decomposition, which enables the achievement of both parameter parsimony and incorporates sparsity effects. The contribution is twofold: first, an extension of multivariate econometric models is provided to account for both tensor-variate response and covariates; second, the effectiveness of the proposed methodology is shown in defining an autoregressive process for time-varying real economic networks. Inference is carried out in the Bayesian framework combined with Monte Carlo Markov Chain (MCMC). Finally, the model is applied to analyse the temporal evolution of real economic networks.

The production of goods and services in modern industrialized economies is organized around complex, interlocking supply chains. Major manufacturing firms, such as Airbus, depend on production ecosystems consisting of thousands of direct and indirect suppliers. It is thus natural to think of the economy as an interdependent network of firms and industries interacting with one another. At the same time, complex supply chains can act as a major source of economic fragility, as disruptions to a few firms can create shortages of essential inputs or destroy accumulated relationship-specific investments. This course provides an overview and synthesis of the research agenda on production networks, with an emphasis on how network relationships in the economy can function as a mechanism for propagation and amplification of shocks.

We will cover the following topics:
1. Production networks and the basics of input-output economics
2. Hulten’s Theorem and production nonlinearities
3. Market imperfections, markups, and distortions
4. Network formation and endogenous production networks
5. Risk, resilience, and fragility of supply chains
6. Application: Monetary policy
7. Empirical evidence
8. Quantitative models
9. Financial networks and contagion

The assessment for the course will be based on exercises/data analyses to be carried on during the course itself or on the discussion of one of the papers in the references.

References

• Acemoglu, Daron, Ufuk Akcigit, and William Kerr (2016), “Networks and the
  macroeconomy: An empirical exploration.” In National Bureau of Economic Research Macroeconomics Annual (Martin Eichenbaum and Jonathan Parker, eds.), volume 30, 276–335, University of Chicago Press.
• Acemoglu, Daron and Pablo D. Azar (2020), “Endogenous production networks.” Econometrica, 88(1), 33–82.
• Acemoglu, Daron, Vasco M. Carvalho, Asuman Ozdaglar, and Alireza Tahbaz-Salehi (2012), “The network origins of aggregate fluctuations.” Econometrica, 80(5), 1977–2016.
• Acemoglu, Daron, Asuman Ozdaglar, and Alireza Tahbaz-Salehi (2015), “Systemic risk and stability in financial networks.” American Economic Review, 105(2), 564–608.
• Acemoglu, Daron, Asuman Ozdaglar, and Alireza Tahbaz-Salehi (2016b), “Networks, shocks, and systemic risk.” In The Oxford Handbook on the Economics of Networks (Yann Bramoulle, Andrea Galeotti, and Brian Rogers, eds.), chapter 21, 569–607, Oxford University Press.
• Acemoglu, Daron, Asuman Ozdaglar, and Alireza Tahbaz-Salehi (2017), “Microeconomic origins of macroeconomic tail risks.” American Economic Review, 107(1), 54–108.
• Acemoglu, Daron and Alireza Tahbaz-Salehi (2025), “The macroeconomics of supply chain disruptions.” Review of Economic Studies, 92, 656–695.
• Allen, Franklin and Douglas Gale (2000), “Financial contagion.” Journal of Political Economy, 108(1), 1–33.
• Atalay, Enghin (2017), “How important are sectoral shocks?” American Economic Journal: Macroeconomics, 9(4), 254–280.
• Bachmann, Rudiger, David Baqaee, Christian Bayer, Moritz Kuhn, Andreas Löschel, Benjamin Moll, Andreas Peichl, Karen Pittel, and Moritz Schularick (2022), “What if? The economic effects for Germany of a stop of energy imports from Russia.” Working paper.
• Baqaee, David and Emmanuel Farhi (2019), “The macroeconomic impact of
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• Baqaee, David and Emmanuel Farhi (2020), “Productivity and misallocation in general equilibrium.” Quarterly Journal of Economics, 135(1), 105–163.
• Baqaee, David and Elisa Rubbo (2023), “Micro propagation and macro aggregation.” Annual Review of Economics, 15(1), 91–123.
• Barrot, Jean-Noel and Julien Sauvagnat (2016), “Input specificity and the propagation of idiosyncratic shocks in production networks.” Quarterly Journal of Economics, 131(3), 1543–1592.
• Bigio, Saki and Jennifer La’O (2020), “Distortions in production networks.” Quarterly Journal of Economics, 135(4), 2187–2253.
• Boehm, Christoph E., Aaron Flaaen, and Nitya Pandalai-Nayar (2019), “Input linkages and the transmission of shocks: Firm-level evidence from the 2011 Tohoku Earthquake.” Review of Economics and Statistics, 101(1), 60–75.
• Buera, Francisco J. and Nicholas Trachter (2024), “Sectoral development multipliers.” NBERWorking Paper No. 32230.
• Capponi, Agostino, Chuan Du, and Joseph E. Stiglitz (2024), “Are supply networks efficiently resilient?” NBER Working Paper No. 32221.
• Carvalho, VascoM., Makoto Nirei, Yukiko Saito, and Alireza Tahbaz-Salehi (2021), “Supply chain disruptions: Evidence from the Great East Japan Earthquake.” Quarterly Journal of Economics, 136(2), 1255–1321.
• Carvalho, Vasco M. and Alireza Tahbaz-Salehi (2019), “Production networks: A primer.” Annual Review of Economics, 11(1), 635–663.
• Carvalho, Vasco M. and Nico Voigtlander (2015), “Input diffusion and the evolution of production networks.” NBER Working Paper No. 20025.
• Dupor, Bill (1999), “Aggregation and irrelevance in multi-sector models.” Journal of Monetary Economics, 43(2), 391–409.
• Elliott, Matthew and Benjamin Golub (2022), “Networks and economic fragility.” Annual Review of Economics, 14, 665–696.
• Elliott, Matthew, Benjamin Golub, and Matthew Jackson (2014), “Financial networks and contagion.” American Economic Review, 104(10), 3115–3153.
• Elliott, Matthew, Benjamin Golub, and Matthew V. Leduc (2022), “Supply network formation and fragility.” American Economic Review, 112(8), 2701–2747. Foerster, Andrew T., Pierre-Daniel G. Sarte, and Mark W. Watson (2011), “Sectoral versus aggregate shocks: A structural factor analysis of industrial production.” Journal of Political Economy, 119(1), 1–38.
• Grossman, Gene M., Elhanan Helpman, and Hugo Lhuillier (2023a), “Supply chain resilience: Should policy promote international diversification or reshoring?” Journal of Political Economy, 131(12), 3462–3496.
• Grossman, Gene M., Elhanan Helpman, and Alejandro Sabal (2023b), “Resilience in vertical supply chains.” NBER Working Paper No. 31739.
• Horvath, Michael (1998), “Cyclicality and sectoral linkages: Aggregate fluctuations from sectoral shocks.” Review of Economic Dynamics, 1(4), 781–808. Horvath, Michael (2000), “Sectoral shocks and aggregate fluctuations.” Journal of Monetary Economics, 45(1), 69–106.
• Jones, Charles I. (2013), “Misallocation, economic growth, and input-output economics.” In Proceedings of Econometric Society World Congress (Daron Acemoglu, Manuel Arellano, and Eddie Dekel, eds.), 419–455, Cambridge University Press.
• Kopytov, Alexandr, Kristoer Nimark, Bineet Mishra, and Mathieu Taschereau-Dumouchel (2024), “Endogenous production networks under supply chain uncertainty.” Econometrica, 92(5), 1621–1659.
• La’O, Jennifer and Alireza Tahbaz-Salehi (2022), “Optimal monetary policy in production networks.” Econometrica, 90(3), 1295–1336.
• Levine, David K. (2012), “Production chains.” Review of Economic Dynamics, 15, 271–282.
• Liu, Ernest (2019), “Industrial policies in production networks.” Quarterly Journal of Economics, 134(4), 1883–1948.
• Long, John B. and Charles I. Plosser (1983), “Real business cycles.” Journal of Political Economy, 91(1), 39–69.
• Obereld, Ezra (2018), “A theory of input-output architecture.” Econometrica, 86(2), 559–589.
• Pasten, Ernesto, Raphael Schoenle, and Michael Weber (2020), “The propagation of monetary policy shocks in a ́heterogeneous production economy.” Journal of Monetary Economics, 116, 1–22.
• Pasten, Ernesto, Raphael Schoenle, and Michael Weber (2024), “Sectoral heterogeneity in nominal price rigidity and the origin of aggregate fluctuations.” American Economic Journal: Macroeconomics, 16(2), 318–352.
• Rubbo, Elisa (2023), “Networks, Phillips curves, and monetary policy.” Econometrica, 91(4), 1417–1455.