(In)Stability for the Blockchain: Deleveraging Spirals and Stablecoin Attacks

We develop a model of stable assets, including non-custodial stablecoins backed by cryptocurrencies. Such stablecoins are popular methods for bootstrapping price stability within public blockchain settings. We derive fundamental results about dynamics and liquidity in stablecoin markets, demonstrate that these markets face deleveraging feedback effects that cause illiquidity during crises and exacerbate collateral drawdown, and characterize stable dynamics of the system under particular conditions. The possibility of such `deleveraging spirals' was first predicted in the initial release of our paper in 2019 and later directly observed during the `Black Thursday' crisis in Dai in 2020. From these insights, we suggest design improvements that aim to improve long-term stability. We also introduce new attacks that exploit arbitrage-like opportunities around stablecoin liquidations. Using our model, we demonstrate that these can be profitable. These attacks may induce volatility in the `stable' asset and cause perverse incentives for miners, posing risks to blockchain consensus. A variant of such attacks also later occurred during Black Thursday, taking the form of mempool manipulation to clear Dai liquidation auctions at near zero prices, costing $8m.Comment: To be published in Cryptoeconomic Systems 202

Optimal Intervention in Economic Networks using Influence Maximization Methods

We consider optimal intervention in the Elliott-Golub-Jackson network model and show that it can be transformed into an influence maximization problem, interpreted as the reverse of a default cascade. Our analysis of the optimal intervention problem extends well-established targeting results to the economic network setting, which requires additional theoretical steps. We prove several results about optimal intervention: it is NP-hard and additionally hard to approximate to a constant factor in polynomial time. In turn, we show that randomizing failure thresholds leads to a version of the problem which is monotone submodular, for which existing powerful approximations in polynomial time can be applied. In addition to optimal intervention, we also show practical consequences of our analysis to other economic network problems: (1) it is computationally hard to calculate expected values in the economic network, and (2) influence maximization algorithms can enable efficient importance sampling and stress testing of large failure scenarios. We illustrate our results on a network of firms connected through input-output linkages inferred from the World Input Output Database

While Stability Lasts: A Stochastic Model of Stablecoins

The `Black Thursday' crisis in cryptocurrency markets demonstrated deleveraging risks in over-collateralized lending and stablecoins. We develop a stochastic model of over-collateralized stablecoins that helps explain such crises. In our model, the stablecoin supply is decided by speculators who optimize the profitability of a leveraged position while incorporating the forward-looking cost of collateral liquidations, which involves the endogenous price of the stablecoin. We formally characterize stable and unstable domains for the stablecoin. We prove bounds on the probabilities of large deviations and quadratic variation in the stable domain and distinctly greater price variance in the unstable domain. The unstable domain can be triggered by large deviations, collapsed expectations, and liquidity problems from deleveraging. We formally characterize a deflationary deleveraging spiral as a submartingale that can cause such liquidity problems in a crisis. We also demonstrate `perfect' stability results in idealized settings and discuss mechanisms which could bring realistic settings closer to the idealized stable settings

Duration-dependent stochastic fluid processes and solar energy revenue modeling

We endow the classical stochastic fluid process with a duration-dependent Markovian arrival process (DMArP). We show that this provides a flexible model for the revenue of a solar energy generator. In particular, it allows for heavy-tailed interarrival times and for seasonality embedded into the state-space. It generalizes the calendar-time inhomogeneous stochastic fluid process. We provide descriptors of the first return of the revenue process. Our main contribution is based on the uniformization approach, by which we reduce the problem of computing the Laplace transform to the analysis of the process on a stochastic Poissonian grid. Since our process is duration dependent, our construction relies on translating duration form its natural grid to the Poissonian grid. We obtain the Laplace transfrom of the project value based on a novel concept of $n$-bridge and provide an efficient algorithm for computing the duration-level density of the $n$-bridge. Other descriptors such as the Laplace transform of the ruin process are further provided

Control of interbank contagion under partial information

International audienceWe consider a stylized core-periphery financial network in which links lead to the creation of projects in the outside economy but make banks prone to contagion risk. The controller seeks to maximize, under budget constraints, the value of the financial system defined as the total amount of external projects. Under partial information on interbank links, revealed in conjunction with the spread of contagion, the optimal control problem is shown to become a Markov decision problem. We find the optimal intervention policy using dynamic programming. Our numerical results show that the value of the system depends on the connectivity in a non- monotonous way: it first increases with connectivity and then decreases with connectivity. The maximum value attained depends critically on the budget of the controller and the availability of an adapted intervention strategy. Moreover, we show that for highly connected systems, it is optimal to increase the rate of intervention in the peripheral banks rather than in core banks. Keywords: Systemic risk, Optimal control, Financial networks

Optimal Control of Interbank Contagion Under Complete Information

International audienceWe study the optimal control of interbank contagion, when the government has complete information on interbank exposures. Financial institutions are prone to insolvency risk channeled through the network of exposures and to liquidity risk through bank runs. The government seeks to maximize, under budget constraints the total value of the financial system or, equivalently, to minimize the dead-weight loss induced by bank runs. The problem can be expressed as a convex optimization problem with a combinatorial aspect, tractable when the set of banks eligible for intervention is sufficiently, yet realistically, smal

Ruin Probabilities for Risk Processes in Stochastic Networks

We study multidimensional Cram\'er-Lundberg risk processes where agents, located on a large sparse network, receive losses form their neighbors. To reduce the dimensionality of the problem, we introduce classification of agents according to an arbitrary countable set of types. The ruin of any agent triggers losses for all of its neighbours. We consider the case when the loss arrival process induced by the ensemble of ruined agents follows a Poisson process with general intensity function that scales with the network size. When the size of the network goes to infinity, we provide explicit ruin probabilities at the end of the loss propagation process for agents of any type. These limiting probabilities depend, in addition to the agents' types and the network structure, on the loss distribution and the loss arrival process. For a more complex risk processes on open networks, when in addition to the internal networked risk processes the agents receive losses from external users, we provide bounds on ruin probabilities.Comment: 31 page

Reinforcement Learning for SBM Graphon Games with Re-Sampling

The Mean-Field approximation is a tractable approach for studying large population dynamics. However, its assumption on homogeneity and universal connections among all agents limits its applicability in many real-world scenarios. Multi-Population Mean-Field Game (MP-MFG) models have been introduced in the literature to address these limitations. When the underlying Stochastic Block Model is known, we show that a Policy Mirror Ascent algorithm finds the MP-MFG Nash Equilibrium. In more realistic scenarios where the block model is unknown, we propose a re-sampling scheme from a graphon integrated with the finite N-player MP-MFG model. We develop a novel learning framework based on a Graphon Game with Re-Sampling (GGR-S) model, which captures the complex network structures of agents' connections. We analyze GGR-S dynamics and establish the convergence to dynamics of MP-MFG. Leveraging this result, we propose an efficient sample-based N-player Reinforcement Learning algorithm for GGR-S without population manipulation, and provide a rigorous convergence analysis with finite sample guarantee

Mean-field BSDEs with jumps and dual representation for global risk measures

International audienceWe study mean-field BSDEs with jumps and a generalized mean-field operator that can capture higher order interactions. We interpret the BSDE solution as a dynamic risk measure for a representative bank whose risk attitude is influenced by the system. This influence can come in a wide class of choices, including the average system state or average intensity of system interactions. Using Fenchel-Legendre transforms, our main result is a dual representation for the expectation of the risk measure in the convex case. In particular we exhibit its dependence on the mean-field operator