Blockchain and Decentralized Finance – BLOCKFI

BLOCKFI mobilizes a resolutely interdisciplinary approach, combining applied mathematics, economics and computer science. On the mathematical side, the project develops stochastic models for the analysis of systemic risk in lending protocols and algorithmic stablecoins, as well as probabilistic modelling tools for Automated Market Makers (AMMs). The statistical analysis of transaction data relies on self-exciting point processes of the Hawkes type, stochastic volatility models and Bayesian algorithms (Sequential Monte Carlo, Approximate Bayesian Computation). On the computer science side, automated formal verification methods -- first-order logic, abductive reasoning -- are employed to certify the behavior of smart contracts. All these approaches are grounded in real data from major decentralized platforms, ensuring the empirical relevance of theoretical developments.

The project's work will produce advances on several complementary fronts. On risk modelling, rigorous mathematical frameworks will be established to quantify the statistical fluctuations of aggregated price estimators in the presence of heavy-tailed data, characteristic of cryptoasset markets. Regarding AMMs, detailed analyses of concentrated liquidity mechanisms will shed light on the trade-offs between liquidity risk and fee revenues for providers. Formal links will also be established between liquidity provision strategies and classical derivative instruments. On the formal verification side, automated reasoning tools will be applied to the analysis of smart contracts, making it possible to identify vulnerability conditions prior to deployment. Finally, statistical models tailored to the specificities of DeFi data -- non-stationarity, heavy tails, missing observations -- will be developed and empirically validated on real data from major decentralized platforms.

The project's prospects are broad and structured around the deepening of each of the four research axes. On systemic risk, network contagion models will be developed and validated against historical data from real incidents. On AMMs, work will continue towards the optimal design of pricing functions and the development of native decentralized options protocols. On formal methods, automated verification tools will be extended to the analysis of interactions between protocols, a major source of vulnerabilities. Finally, the statistical axis will move towards real-time detection of anomalies and market manipulation. In the longer term, BLOCKFI aims to contribute actively to European regulatory debates on digital assets, providing solid scientific foundations for ongoing legislative work.

The project has already generated and will continue to generate significant scientific output, in the form of articles in leading international journals in financial mathematics, statistics and theoretical computer science. All code and tools developed will be made available to the community via public GitHub repositories. No patents are planned, in keeping with the academic and open-source nature of the project.

The concept of Decentralized Finance (DeFi) involves applications operating on blockchains, aiming to replicate traditional financial products. Despite being smaller in volume compared to Traditional Finance (TradFi), DeFi is gaining significance in the crypto landscape. DeFi addresses key issues of TradFi. In TradFi, assets are entrusted to intermediaries, leading to trust and counterparty risks. TradFi settlements are slow due to multiple intermediaries, while DeFi settles assets within seconds, operating 24/7. DeFi applications are interoperable, enabling seamless asset flow and offering properties like censorship resistance and transparency. DeFi is poised to underpin disintermediated finance, demanding extensive research.

This ANR proposal aims to develop mathematical and statistical models, and tools for risk monitoring of DeFi protocols, ground execution protocols on formal proofs, and enhance next-gen protocols' efficiency and security.
Among the topics that will be investigated, let us mention systemic risks for stablecoins and lending-borrowing protocols, Automated Market Makers and the development of formal methods and suitable statistical models. The interdisciplinary team of mathematicians, statisticians, economists, and computer scientists is a strong asset for this project.