Related papers: A Dynamical Systems Approach to Cryptocurrency Sta…
This work is concerned with the stability properties of linear stochastic differential equations with random (drift and diffusion) coefficient matrices, and the stability of a corresponding random transition matrix (or exponential…
This article concerns the stability of a model for mass-spring systems with positive damping and negative stiness. It is well known that when the coefficients are frozen in time the system is unstable. Here we find conditions on the…
Mathematical modeling of fluid dynamics for computer graphics requires high levels of theoretical rigor to ensure visually plausible and computationally efficient simulations. This paper presents an in-depth theoretical framework analyzing…
In decentralized finance (DeFi), stablecoins like DAI are designed to offer a stable value amidst the fluctuating nature of cryptocurrencies. We examine the class of crypto-backed stable derivatives, with a focus on mechanisms for price…
The goal of this paper is to explore the relationship between momentum effects and liquidity in cryptocurrency markets. Portfolios based on momentum-liquidity bivariate sorts are formed and rebalanced on a varying number of cryptocurrencies…
Concepts like `typicality' and the `eigenstate thermalization hypothesis' aim at explaining the apparent equilibration of quantum systems, possibly after a very long time. However, these concepts are not concerned with the specific way in…
Stablecoins have emerged as a significant component of global financial infrastructure, with aggregate market capitalization surpassing USD250 billion in 2025. Their increasing integration into payment and settlement systems has…
Cryptocurrencies are considered relevant assets and they are currently used as an investment or to carry out transactions. However, specific characteristics commonly associated with the cryptocurrencies such as irreversibility,…
We model incentive security in non-custodial stablecoins and derive conditions for participation in a stablecoin system across risk absorbers (vaults/CDPs) and holders of governance tokens. We apply option pricing theory to derive closed…
Although classical economic theory is based on the concept of stable equilibrium, real economic systems appear to be always out of equilibrium. Indeed, they share many of the dynamical features of other complex systems, e.g., ecological…
This paper considers discontinuous dynamical systems, i.e., systems whose associated vector field is a discontinuous function of the state. Discontinuous dynamical systems arise in a large number of applications, including optimal control,…
Cryptocurrency is a form of digital currency using cryptographic techniques in a decentralized system for secure peer-to-peer transactions. It is gaining much popularity over traditional methods of payments because it facilitates a very…
During a financial crisis, the capital markets network frequently exhibits a high correlation between returns. We developed a network analysis framework based on daily returns from 42 countries to determine systemic stability. Our network…
Dynamically distributed inflation is a common mechanism used to guide a blockchain's staking rate towards a desired equilibrium between network security and token liquidity. However, the high sensitivity of the annual percentage yield to…
Cryptocurrencies have evolved into an important asset class, providing a variety of benefits. However, they also present significant risks, such as market volatility and the potential for misuse in illegal activities. These risks underline…
The Holy Grail of a decentralised stablecoin is achieved on rigorous mathematical frameworks, obtaining multiple advantageous proofs: stability, convergence, truthfulness, faithfulness, and malicious-security. These properties could only be…
This paper deals with mathematical models of continuous crystallization described by hyperbolic systems of partial differential equations coupled with ordinary and integro-differential equations. The considered systems admit nonzero…
We consider the stability of a system of equations which are a singular perturbation of the incompressible rigid-plastic flow equations used to model granular flow. A linear stability analysis shows that solutions of these equations are…
We organize existing empirical regularities of cryptocurrencies into seven stylized facts and analyze cryptocurrencies through the lens of empirical asset pricing. We find important similarities with traditional markets--risk-adjusted…
In recent years decentralized currencies developed through Blockchains are increasingly becoming popular because of their transparent nature and absence of a central controlling authority. Though a lot of computation power, disk space, and…