Talks and Abstracts

Financial Macroeconomics and Climate Change by Gaël Giraud

In this course, I present and discuss an emerging trend in the literature around stock-flow consistent dynamical models combining financial macrodynamics, climate models and geophysical models of natural resources. We will explore some of the mathematical challenges as well as policy-oriented outcomes.
Key questions will be:

1. the linkage between income inequality, macro-dynamics and GHG emissions;
2. the spatialization of the economic impact of global warming;
3. the interplay between the need for green infrastructures for mitigation purposes and the growing scarcity of a number of minerals.

BLOCKASTICS – Stochastic models for blockchain analysis by Pierre-Olivier Goffard

In 2008, Blockchain was introduced to the world as the underlying technology of the Bitcoin electronic cash system. After more than a decade of development, various blockchain systems have been proposed with application going beyond the creation of a cryptocurrency. This course is organized around four 45-minute lectures on the theme of stochastic models in relation to the analysis of blockchain systems.

Part 1: Blockchain concepts 

A blockchain is a distributed data ledger maintained by achieving consensus among a number of nodes in Peer-to-peer network. After providing some preliminary definitions, we introduce theproof-of-work and proof-of-stake consensus protocols which are at the core of public and permissionless blochchains (like the bitcoin and ethereum ones). We further define three dimensions according to which a blockchain system may be evaluated including (1) efficiency, (2) decentralization and (3) security.

Part 2: Simple models for blockchain performance analysis

A review of the mathematical models and tools used so far to assess the performance of blockchain systems is provided. They consist of standard models from the applied probability literature like random walks, Markov chains, urns and queues.

Part 3: Risk models and blockchain mining

Mining blocks on a blockchain equipped with a proof of work consensus protocol is well-known to be resource-consuming. A miner bears the operational cost, mainly

electricity consumption and IT gear, of mining, and is compensated by a capital gain when a block is discovered. The profitability of mining is studied via stochastic models and tools borrowed from insurance risk theory. We consider the case of solo mining, pool mining and selfish mining.

Part 4: Decentralized finance and cryptoasset pricing

Blockchain creates an environment where multiple parties can interact directly and transparently. It is therefore immediately relevant to banks and financial institutions which incur huge middlemen costs in settlements and other back office operations. Decentralized finance (DeFi) offers a new financial architecture that is non-custodial, permissionless, openly auditable, pseudo-anonymous and with potential new capital efficiencies. An overview of the existing cryptoassets is given before discussing some pricing models for this new class of financial assets.

Website for the Mini-Course: Materials and Syllabus can be downloaded here.

Mean-Field Dynamics and Machine Learning by Xin Guo and Renyuan Xu

In this short course, we discuss how mean-field theory can be exploited to build the mathematical foundation in several topical areas of machine learning, including multi-agent reinforcement learning and the training of neural networks.

The course will start with the basics of reinforcement learning, deep learning, stochastic games, and mean-field theory. It will then introduce the mathematical framework of mean-field games (MFGs) and mean-field controls (MFCs) with learning, the approximation MFG/MFC to multi-agent reinforcement learning, time consistency and computational complexity issues in their algorithmic designs. Next, it will demonstrate how mean-field theory helps to better understand and improve the training procedures of several neural network architectures such as residual networks (ResNet) and generative adversarial networks (GANs).

Blockchains and distributed ledgers: the underlying mathematics, economics, and technology by Alexander Lipton

In this short course, we discuss some of the most recent developments in the cryptocurrency ecosystem. Specifically, we review basic concepts related to blockchains and distributed ledgers. We discuss the behavior of cryptocurrencies such as Bitcoin and Ethereum. We also study stable coins, their classification, potential applications, and related topics. We also address the emerging field of DeFi (Decentralized Finance), including Automated Market Makers (AMM), yield farmers, and other peculiar concepts. We explain mathematics, economics, and technology behind these developments and elaborate on their pros and cons.

Introduction to Climate Finance by Peter Tankov

The emerging field of climate finance is developing around two key challenges. The first one is to understand how the financial sector may contribute to the energy transition, by measuring its impact on the environment, developing suitable financial instruments to attract funding to green assets, and aligning the financial portfolios with the international climate objectives. The second one is to quantify and manage the financial climate risks: the long-term threats for the financial sector and the economy in general posed by climate change. Key features of this new field are its multidisciplinary nature since it requires contributions from economists, mathematicians, quantitative finance specialists, climatologists, engineers etc., and its reliance on a multitude of financial and extra-financial data sources of much greater variety than in traditional finance. In these lectures we will give an overview of the main challenges of climate finance and some of the economic and mathematical tools to address them.

Part 1: Introduction

Part 2: Climate financial risks

Physical risks and climate scenarios. Transition risks and integrated assessment model (IAM) scenarios. Scenario uncertainty. Climate stress testing.

Part 3: Investor impact

Measuring the environmental impact of economic activities. Company impact vs. investor impact. Climate impact investing. Collective impact of investors.

Part 4: Portfolio alignment to a 2°C trajectory and net zero targets