Related papers: The Geometry of Constant Function Market Makers
The paper studies a general scheme for constructing metrics on a product of metric spaces by means of a family of continuous convex functions. This construction includes the conventional $p$-metrics and generates metrics that are…
This paper demonstrates that Automated Market Maker (AMM) based markets, such as those using constant product formulas (e.g., Uniswap), are inherently path-dependent. We prove mathematically that the sequence of operations in AMMs…
An automated market maker (AMM) provides a method for creating a decentralized exchange on the blockchain. For this purpose, individual investors lend liquidity to the AMM pool in exchange for a stream of fees earned from its operations as…
Decentralized Finance (DeFi) applications introduce novel financial instruments replicating and extending traditional ones through blockchain-based smart contracts. Among these applications, DeFi derivatives protocols enable the creation…
Piecewise smooth systems are intensively studied today in many application areas, such as economics, finance, engineering, biology, and ecology. In this work, we consider a class of one-dimensional piecewise linear discontinuous maps with a…
In this paper, the notion of $\mathbb{C}$-simulation function is introduced and the existence and uniqueness of common fixed points of two self-mappings satisfying contractive conditions in the setting of complex valued metric spaces via…
Tradable mobility credit (TMC) schemes are an approach to travel demand management that have received significant attention in recent years. This paper proposes and analyzes alternative market models for a TMC system -- focusing on market…
This paper presents an agent-based artificial cryptocurrency market in which heterogeneous agents buy or sell cryptocurrencies, in particular Bitcoins. In this market, there are two typologies of agents, Random Traders and Chartists, which…
Although machine learning approaches have been widely used in the field of finance, to very successful degrees, these approaches remain bespoke to specific investigations and opaque in terms of explainability, comparability, and…
We discuss how minimal financial market models can be constructed by bridging the gap between two existing, but incomplete, market models: a model in which a population of virtual traders make decisions based on common global information…
The goal of cryptocurrencies is decentralization. In principle, all currencies have equal status. Unlike traditional stock markets, there is no default currency of denomination (fiat), thus the trading pairs can be set freely. However, it…
Flexible modelling of the autocovariance function (ACF) is central to time-series, spatial, and spatio-temporal analysis. Modern applications often demand flexibility beyond classical parametric models, motivating non-parametric…
The alternating direction method of multipliers (ADMM) algorithm is a powerful and flexible tool for complex optimization problems of the form $\min\{f(x)+g(y) : Ax+By=c\}$. ADMM exhibits robust empirical performance across a range of…
In blockchains such as Bitcoin and Ethereum, users compete in a transaction fee auction to get their transactions confirmed in the next block. A line of recent works set forth the desiderata for a "dream" transaction fee mechanism (TFM),…
Centralized monetary policy, leading to persistent inflation, is often inconsistent, untrustworthy, and unpredictable. Algorithmic stablecoins enabled by blockchain technology are promising in solving this problem. Algorithmic stablecoins…
Decentralized payment systems such as Bitcoin have become massively popular in the last few years, yet there is still much to be done in understanding their formal properties. The vast majority of decentralized payment systems work by…
As an integral part of the decentralized finance (DeFi) ecosystem, decentralized exchanges (DEXs) with automated market maker (AMM) protocols have gained massive traction with the recently revived interest in blockchain and distributed…
Blockchain technology and, in particular, blockchain-based cryptocurrencies offer us information that has never been seen before in the financial world. In contrast to fiat currencies, all transactions of crypto-currencies and crypto-tokens…
The non-fungible token (NFT) market emerges as a recent trading innovation leveraging blockchain technology, mirroring the dynamics of the cryptocurrency market. The current study is based on the capitalization changes and transaction…
In this paper, considering a wider class of simulation functions some fixed point results for multivalued mappings in $\alpha$-complete metric spaces have been presented. Results obtained in this paper extend and generalize some well-known…