Blockchain and Decentralized Finance

Decentralised Finance (DeFi) refers to applications running on public blockchains that aim to replicate and extend some traditional financial functionalities without relying on centralised intermediaries. Over the last decade, DeFi has grown at a rapid pace, giving rise to algorithmic and financial innovations with spillover effects beyond the boundaries of crypto markets alone.

Unlike traditional finance (TradFi), which depends on banks, brokers, and regulated exchanges, DeFi protocols operate through smart contracts: self-executing code deployed on a blockchain. This enables permissionless lending and borrowing, accessible staking, and has led to the emergence of decentralised exchanges taking unprecedented forms — all running transparently and continuously, without human intermediaries. While this opens remarkable possibilities, it also introduces new theoretical and practical questions.

The mathematical and statistical modelling of DeFi protocols remains in its infancy. Rigorous quantitative methods are needed to understand the structural properties of these systems, assess their risks, and design more robust next-generation protocols. The ANR BlockFi project addresses this gap by fostering the development of mathematical models, statistical tools, and formal verification methods. Topics under study include the design of interest rate models on lending protocols, the mechanics of automated market makers (AMMs), the application of formal proofs to protocols, asset management questions in the DeFi world, and the study of systemic risk.

To tackle these challenges, we have assembled an interdisciplinary team of mathematicians, statisticians, economists, and computer scientists. Beyond producing research, our ambition is to make these emerging scientific questions visible to the broader academic community and to train the next generation of researchers.