相关论文: The Geometry of Constant Function Market Makers
Perpetual futures are the most popular cryptocurrency derivatives. Perpetuals offer leveraged exposure to their underlying without rollover or direct ownership. Unlike fixed-maturity futures, perpetuals are not guaranteed to converge to the…
Decentralized exchanges (DEXs) face persistent challenges in liquidity retention and user engagement due to inefficiencies in conventional automated market maker (AMM) designs. This work proposes a dual-mechanism framework to address these…
Geometric mean market makers (G3Ms), such as Uniswap and Balancer, comprise a popular class of automated market makers (AMMs) defined by the following rule: the reserves of the AMM before and after each trade must have the same (weighted)…
Liquidity providers are essential for the function of decentralized exchanges to ensure liquidity takers can be guaranteed a counterparty for their trades. However, liquidity providers investing in liquidity pools face many risks, the most…
The Functional Machine Calculus (FMC, Heijltjes 2022) extends the lambda-calculus with the computational effects of global mutable store, input/output, and probabilistic choice while maintaining confluent reduction and simply-typed strong…
Blockchain is a decentralized system that allows transaction transmission and storage according to the roles of the Consensus algorithm and Smart contracts. Non-fungible tokens (NFTs) consolidate the best characteristics of blockchain…
We focus on the problem of market making in high-frequency trading. Market making is a critical function in financial markets that involves providing liquidity by buying and selling assets. However, the increasing complexity of financial…
Stablecoins, which are primarily intended to function as a global reserve of value are insubstantial in their design and present many failure points. The primary mechanism to enable these coins to hold on to a fixed value is by backing them…
We establish existence of Predictable Forward Performance Processes (PFPPs) in complete markets, which has been previously shown only in the binomial setting. Our market model can be a discrete-time or a continuous-time model, and the…
Current approaches to the cryptocurrency automated market makers result in poor impermanent loss and capital efficiency. We analyze the mechanics underlying DODO Exchange's proactive market maker (PMM) to probe for solutions to these…
Symmetry-informed machine learning can exhibit advantages over machine learning which fails to account for symmetry. In the context of continuous symmetry detection, current state of the art experiments are largely limited to detecting…
Decentralized exchange platforms such as Uniswap and Balancer operate on several pools where each pool contains two or more cryptocurrencies and constitutes direct trading pairs. The drawbacks here are that liquidity providing requires…
The Geometric Brownian Motion (GBM) is a standard model in quantitative finance, but the potential function of its stochastic differential equation (SDE) cannot include stable nonzero prices. This article generalises the GBM to an SDE with…
Automated Market Makers (AMMs) are decentralized exchange protocols that provide continuous access to token liquidity without the need for order books or traditional market makers. However, this innovation has failed to scale when it comes…
We present a mathematical model of a market with $m$ shares traded across $n$ investor groups, each one with similar motivations and trading strategies. The market of each asset consists of a fixed amount of cash and shares (no additions…
This paper mathematically models a constant-function automated market maker (CFAMM) position as a portfolio of exotic options, known as perpetual American continuous-installment (CI) options. This model replicates an AMM position's delta at…
The Functional Machine Calculus (FMC), recently introduced by the authors, is a generalization of the lambda-calculus which may faithfully encode the effects of higher-order mutable store, I/O and probabilistic/non-deterministic input.…
Stablecoins serve as the fundamental infrastructure for Decentralised Finance (DeFi), acting as the primary bridge between fiat currencies and the digital asset ecosystem. While peg stability is well-documented, the structural role…
This paper derives new algorithms for signomial programming, a generalization of geometric programming. The algorithms are based on a generic principle for optimization called the MM algorithm. In this setting, one can apply the…
A generalized continuous economic model is proposed for random markets. In this model, agents interact by pairs and exchange their money in a random way. A parameter controls the effectiveness of the transactions between the agents. We show…