arXiv subjects

Mikhail Perepelitsa

Publications and source records attributed to Mikhail Perepelitsa.

5 recordsLinked to original sources

arXiv2026

Proof-of-Stake Dynamics: The Elusive Price Anchor and Endogenous Volatility Harvesting

In this paper, we develop an open-economy macroeconomic model of a Proof-of-Stake network to analyze nominal token-price dynamics and the systemic effects of speculative capital. We first consider a network populated solely by active utility users, who finance network activity through a steady exogenous inflow of fiat currency. We prove the existence of a unique, globally asymptotically stable steady-state equilibrium with a well-defined nominal token price and derive a closed-form expression for the network's relaxation time. Calibrating the model using parameters representative of the current Ethereum network, we estimate a relaxation half-life of approximately 46 years. This extreme macroeconomic inertia implies that the token price may remain persistently displaced from its evolving steady-state benchmark, producing sustained price overshooting as the network adjusts to changing fundamentals. We then introduce an Investor class to examine the effects of passive and active speculative capital. We show that passive institutional staking compresses the native staking yield and creates a structural imbalance that systematically raises the nominal token price while shifting consensus ownership away from active utility users. Active speculative capital has a qualitatively different effect. In response to capital shocks, the Consumer class's rigid preference for fiat-denominated consumption generates an endogenous constant-value strategy. This mechanism shifts staked-token ownership from the Investor class toward active utility users, with potentially favorable implications for consensus decentralization.

econ.GN↗

arXiv2026

Bubbles vs. Baselines: Token Valuation and Institutional Capital in PoS Networks under EIP-1559

This paper presents an open-economy macroeconomic equilibrium model for Proof-of-Stake (PoS) networks with fee-burn mechanics (EIP-1559) that formalizes the strategic interplay between a Kelly-optimizing rational institutional investor and a utility-driven retail consumer. We analyze network dynamics across two behavioral regimes. In The Unbounded Accumulation Model, the consumer purely accumulates tokens, creating an exclusive buy-side pressure that interacts with institutional portfolio rebalancing to fuel an ever-expanding speculative bubble and generate compounding excess returns for investors. Conversely, in The Utility-Consumption Model, the consumer dynamically buys and sells tokens to balance crypto wealth against real-world fiat consumption. Within this framework, we derive an explicit steady-state equilibrium price for ETH, demonstrating how token valuation anchors to a stable fundamental baseline that scales directly with network adoption while completely dissolving the institutional yield premium. Our numerical simulations show that while exogenous traditional finance (TradFi) shocks propagate through portfolio rebalancing to drive high token price volatility, network inflation remains highly stable. Furthermore, we prove that network security is insulated from institutional monopoly by counter-cyclical consumer behavior. Our findings reveal that institutional excess wealth creation in PoS ecosystems is not native to the staking protocol itself, but is strictly driven by the leveraged extraction of the retail consumer's continuous demand for transactional utility.

q-fin.MF↗

arXiv2026

The Financialization of Proof-of-Stake: Asymptotic Centralization under Exogenous Risk Premiums

This paper introduces a heterogeneous macroeconomic model of a Proof-of-Stake (PoS) network to analyze the long-term centralizing effects of external traditional finance (TradFi) yields. We model a continuum of rational actors divided into two distinct classes: investors, who optimize portfolios between staking and external variance-dominated investments, and consumers, who balance staking yields against the transactional utility of holding liquid assets. By employing a quasi-linear utility function to model consumer behavior, we derive a cubic polynomial that strictly defines the unique macroeconomic equilibrium of the coupled network. The model demonstrates that, at scale, external macroeconomic factors force the complete institutional capture of the PoS consensus layer. Because investors have access to external risk premiums, their wealth compounds exponentially, leading to massive capital inflows that crush the protocol's internal staking yield to effectively zero. We show that as the yield is crushed, consumer wealth becomes strictly upper-bounded. Ultimately, consumers are forced to cease staking entirely and hold all remaining wealth in liquid form to satisfy their transactional constraints.

q-fin.GN↗

arXiv2014

Vanishing Viscosity Solutions of the Compressible Euler Equations with Spherical Symmetry and Large Initial Data

We are concerned with spherically symmetric solutions of the Euler equations for multidimensional compressible fluids, which are motivated by many important physical situations. Various evidences indicate that spherically symmetric solutions of the compressible Euler equations may blow up near the origin at certain time under some circumstance. The central feature is the strengthening of waves as they move radially inward. A longstanding open, fundamental question is whether concentration could form at the origin. In this paper, we develop a method of vanishing viscosity and related estimate techniques for viscosity approximate solutions, and establish the convergence of the approximate solutions to a global finite-energy entropy solution of the compressible Euler equations with spherical symmetry and large initial data. This indicates that concentration does not form in the vanishing viscosity limit, even though the density may blow up at certain time. To achieve this, we first construct global smooth solutions of appropriate initial-boundary value problems for the Euler equations with designed viscosity terms, an approximate pressure function, and boundary conditions, and then we establish the strong convergence of the viscosity approximate solutions to a finite-energy entropy solutions of the Euler equations.

math.AP↗

arXiv2009

Vanishing Viscosity Limit of the Navier-Stokes Equations to the Euler Equations for Compressible Fluid Flow

We establish the vanishing viscosity limit of the Navier-Stokes equations to the isentropic Euler equations for one-dimensional compressible fluid flow. For the Navier-Stokes equations, there exist no natural invariant regions for the equations with the real physical viscosity term so that the uniform sup-norm of solutions with respect to the physical viscosity coefficient may not be directly controllable and, furthermore, convex entropy-entropy flux pairs may not produce signed entropy dissipation measures. To overcome these difficulties, we first develop uniform energy-type estimates with respect to the viscosity coefficient for the solutions of the Navier-Stokes equations and establish the existence of measure-valued solutions of the isentropic Euler equations generated by the Navier-Stokes equations. Based on the uniform energy-type estimates and the features of the isentropic Euler equations, we establish that the entropy dissipation measures of the solutions of the Navier-Stokes equations for weak entropy-entropy flux pairs, generated by compactly supported $C^2$ test functions, are confined in a compact set in $H^{-1}$, which lead to the existence of measure-valued solutions that are confined by the Tartar-Murat commutator relation. A careful characterization of the unbounded support of the measure-valued solution confined by the commutator relation yields the reduction of the measure-valued solution to a Delta mass, which leads to the convergence of solutions of the Navier-Stokes equations to a finite-energy entropy solution of the isentropic Euler equations.

math.AP↗