2021 SUMMER SCHOOL

21-24 September 2021

The BFS summer school 2021 aims to bring advanced Master students, PhD and Postdoctoral students to the front of current research topics in financial mathematics.

This summer school is dedicated to honour the memory of Tomas Björk (1947-2021).

The Organising Committee has identified the following fields of interest:

  • Green Finance
  • Decentralized Finance
  • Mean field approaches and Optimization

Invited speakers

  • Gaël Giraud, France CNRS (National Center for Scientific Research) and Georgetown University
  • Pierre-Olivier Goffard, Université Claude Bernard Lyon 1
  • Xin Guo, University of California Berkeley
  • Alex Lipton, Sila, Hebrew University of Jerusalem and MIT
  • Peter Tankov, ENSAE
  • Renyuan Xu, Oxford University

Organising Committee

  • Francesca Biagini
  • Jean-Pierre Fouque
  • Matheus Grasselli
  • Mathieu Rosenbaum
  • Josef Teichmann

Registration

Registration is compulsory and free for members of the Bachelier Finance Society.
For non-members we charge 60$. You can become a member here.

Registration is now closed.

Gaël Giraud

a picture of the speaker gael giraudGaël Giraud is  a senior researcher at the France CNRS (National Center for Scientific Research) and professor at the MacCourt School of Public Policy (Georgetown university). After having served as chief economist of the French Development Bank, he is founding a Program for Environmental Justice at Georgetown university.




His website


Pierre-Olivier Goffard

a picture of the speaker pierre-olivier goffard

Pierre-Olivier Goffard is an associate professor at l’Institut de Science Financière et d’Assurances, a graduate school specialized in actuarial science part of Université Claude Bernard Lyon 1. His research interests lie in the interplay of statistics and probability applied to insurance and finance. He has focused recently on the study of blockchain systems using stochastic models.




His website


Xin Guo

a picture of the speaker xin guo

Xin Guo is a Coleman Fung Chair professor at UC Berkeley and an Amazon scholar; Renyuan Xu is a Hooke research fellow at the math institute of Oxford University.






Her website


Alex Lipton

a picture of the speaker alex lipton

Alexander Lipton is Co-Founder and Chief Information Officer at Sila, Partner at Numeraire Financial, Visiting Professor and Dean’s Fellow at the Hebrew University of Jerusalem, and Connection Science Fellow at MIT. He is a Board Member at Sila (Oregon) and an Advisory Board Member at numerous Fintech companies worldwide.
His scientific interests are centered on cryptocurrencies, distributed ledgers, decentralized finance, quantitative development of asset allocation theory, modern monetary circuit theory, central clearing, and related topics.
In 2000 Alex was awarded the first-ever Quant of the Year Award by Risk Magazine; in 2021, he was awarded the Buy-Side Quant of the Year Award (jointly with Marcos Lopez de Prado).

His extended bio


Peter Tankov

a picture of the speaker peter tankov

Peter Tankov is professor of quantitative finance at ENSAE, the French national school for statistics and economic administration, having previously worked at Paris-Diderot (Paris 7) university and Ecole Polytechnique. His current research interests include theory and applications of mean-field games, quantitative finance, energy finance, and green and sustainable finance. Peter is the author of over 50 research articles on these and other topics and of the widely read book, Financial Modelling with Jump Processes. He is the recipient of the 2016 Best Young Researcher in Finance award of the Europlace Institute of Finance and the principal investigator of several national grants. Peter is the scientific
director of the Green and Sustainable Finance Research Program at Louis Bachelier Institute, member of the board of directors of GRASFI, the Global Research Alliance for Sustainable Finance and and Investment, and member of editorial boards of the main quantitative finance journals: Mathematical Finance, Finance and Stochastics and SIAM Journal on Financial Mathematics.

His website


Renyuan Xu

a picture of the speaker renyuan xu

Renyuan Xu is currently a Hooke Research Fellow in the Mathematical Institute at the University of Oxford. She completed her Ph.D. degree in Operations Research from UC Berkeley in 2019. She will join the Epstein Department of Industrial Systems Engineering at the University of Southern California as a Gabilan Assistant Professor in Fall 2021. Her research interests lie at the intersection of machine learning, stochastic control, game theory, and mathematical finance.



Her website

Each day consists of 6 lectures of 45 min = 4.5 hours
EDT = Eastern Daylight Time (= UTC-4)

Day 1: Tuesday, 21 September 2021

Timezone Time Speaker Title
EDT 7:30 Pierre-Olivier Goffard Blockchain concepts
EDT 8:15 Peter Tankov Introduction to climate finance
EDT 9:00 Break
EDT 9:15 Peter Tankov Introduction to climate finance
EDT 10:00 Alex Lipton Blockchains and distributed ledgers: the underlying mathematics, economics, and technology
EDT 10:45 Break
EDT 11:30 Renyuan Xu Mean-Field Dynamics and Machine Learning
EDT 12:15 Xin Guo Mean-Field Dynamics and Machine Learning
EDT 13:00 Théo Le Guenedal Tutorial: Climate data and details of models discussed in the session by Peter Tankov

Day 2: Wednesday, 22 September 2021

Timezone Time Speaker Title
EDT 7:30 Pierre-Olivier Goffard Simple models for blockchain performance analysis
EDT 8:15 Gaël Giraud Financial Macroeconomics and Climate Change
EDT 9:00 Break
EDT 9:15 Gaël Giraud Financial Macroeconomics and Climate Change
EDT 10:00 Alex Lipton Blockchains and distributed ledgers: the underlying mathematics, economics, and technology
EDT 10:45 Break
EDT 11:30 Renyuan Xu Mean-Field Dynamics and Machine Learning
EDT 12:15 Xin Guo Mean-Field Dynamics and Machine Learning

Day 3: Thursday, 23 September 2021

Timezone Time Speaker Title
EDT 7:30 Pierre-Olivier Goffard Risk models and blockchain mining
EDT 8:15 Peter Tankov Introduction to climate finance
EDT 9:00 Break
EDT 9:15 Gaël Giraud Financial Macroeconomics and Climate Change
EDT 10:00 Alex Lipton Blockchains and distributed ledgers: the underlying mathematics, economics, and technology
EDT 10:45 Break
EDT 11:30 Renyuan Xu Mean-Field Dynamics and Machine Learning
EDT 12:15 Xin Guo Mean-Field Dynamics and Machine Learning

Day 4:Friday, 24 September 2021

Timezone Time Speaker Title
EDT 7:30 Pierre-Olivier Goffard Decentralized finance and cryptoasset pricing
EDT 8:15 Peter Tankov Introduction to climate finance
EDT 9:00 Break
EDT 9:15 Gaël Giraud Financial Macroeconomics and Climate Change
EDT 10:00 Alex Lipton Blockchains and distributed ledgers: the underlying mathematics, economics, and technology
EDT 10:45 Break
EDT 11:30 Renyuan Xu Mean-Field Dynamics and Machine Learning
EDT 12:15 Xin Guo Mean-Field Dynamics and Machine Learning

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


Venues

Will be held online on Zoom.