Axioms for Automated Market Makers: A Mathematical Framework in FinTech and Decentralized Finance

Bichuch, Maxim; Feinstein, Zachary

doi:10.48550/arxiv.2210.01227

Cited by 2 publications

(2 citation statements)

References 9 publications

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“…While fees could be easily integrated into our model, they have no bearing on complexity-approximation trade-offs and thus we generally ignore them in this paper for simplicity. Some previous papers propose generalizations of CFMMs to somewhat wider classes of exchanges (Bichuch and Feinstein 2022;Xu et al 2021) without considering LOBs.…”

Section: Literature Reviewmentioning

confidence: 99%

Complexity-Approximation Trade-offs in Exchange Mechanisms: AMMs vs. LOBs

Milionis¹,

Moallemi²,

Roughgarden³

2023

Preprint

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This paper presents a general framework for the design and analysis of exchange mechanisms between two assets that unifies and enables comparisons between the two dominant paradigms for exchange, constant function market markers (CFMMs) and limit order books (LOBs). In our framework, each liquidity provider (LP) submits to the exchange a downward-sloping demand curve, specifying the quantity of the risky asset it wishes to hold at each price; the exchange buys and sells the risky asset so as to satisfy the aggregate submitted demand. In general, such a mechanism is budget-balanced (i.e., it stays solvent and does not make or lose money) and enables price discovery (i.e., arbitrageurs are incentivized to trade until the exchange's price matches the external market price of the risky asset). Different exchange mechanisms correspond to different restrictions on the set of acceptable demand curves.The primary goal of this paper is to formalize an approximation-complexity trade-off that pervades the design of exchange mechanisms. For example, CFMMs give up expressiveness in favor of simplicity: the aggregate demand curve of the LPs can be described using constant space (the liquidity parameter), but most demand curves cannot be well approximated by any function in the corresponding single-dimensional family. LOBs, intuitively, make the opposite trade-off: any downward-slowing demand curve can be well approximated by a collection of limit orders, but the space needed to describe the state of a LOB can be large.This paper introduces a general measure of exchange complexity, defined by the minimal set of basis functions that generate, through their conical hull, all of the demand functions allowed by an exchange. With this complexity measure in place, we investigate the design of optimally expressive exchange mechanisms, meaning the lowest complexity mechanisms that

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Section: Literature Reviewmentioning

confidence: 99%

Complexity-Approximation Trade-offs in Exchange Mechanisms: AMMs vs. LOBs

Milionis¹,

Moallemi²,

Roughgarden³

2023

Preprint

View full text Add to dashboard Cite

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“…An algorithm has been conceived following the main guidelines of an AMM for the full collateralization of invoices. As previously stated, AMM were designed to trade two assets by their balance x and y in a liquidity pool to keep up a constant k, as x • y = k, so that incoming x means withdrawing y to keep the x • y constant at k. There are several variants of the same scheme [33] to add resilience and utility to the AMM implementation, which must follow their axioms.…”

Section: Reverse Kelly Amm (Rkamm) Designmentioning

confidence: 99%

Invoice Discounting Using Kelly Criterion by Automated Market Makers-like Implementations

Rosa

El-Fakdi

Ballesteros-Rodríguez

2023

Mathematics

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Funding shortages are a persistent issue, particularly for small and medium-sized enterprises (SMEs), and the problem tends to worsen cyclically. The market for factoring and invoice discounting aims to address delays in payment for commercial invoices. These involves sellers present unpaid invoices to financial organizations, typically banks, who provide an advance payment. The implementations of the factoring services without intermediaries in blockchain of the state of the art are all based on the publication on-chain of all the invoices, use know your customer (KYC) mechanisms, and over-collateralize the invoices. This article proposes a new, decentralized approach to lending services that completely eliminates intermediaries and does not require strong KYC, yet it is reasonably resilient. The approach uses liquidity pools and associated heuristics to create a model of risk compensation. In this model, a formula measures the contributed collateral to an invoice and the risk of a late invoice or non-payment, using the Kelly criterion to calculate the optimal premium for funding said invoice in the liquidity pool. The algorithm’s performance is tested in many scenarios involving several invoice amounts, collaterals, payment delays, and non-payment rates. The study also examines premium distribution policies and hack scenarios involving bogus, non-payable invoices. The outcome is a decentralized market that uses the Kelly criterion and is reasonably resilient to a wide range of invoicing scenarios, including 5% non-payment rates and 10% bogus invoices, yet provides a sound profit to liquidity providers. The algorithm’s resilience is enhanced by several premium distribution policies over partially collateralized invoices from 50 to 70%, resulting in optimal premium withdrawal policies every 30 days, making it the first protocol for loanable funds that does not require over-collateralization to be profitable and resilient.

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Axioms for Automated Market Makers: A Mathematical Framework in FinTech and Decentralized Finance

Cited by 2 publications

References 9 publications

Complexity-Approximation Trade-offs in Exchange Mechanisms: AMMs vs. LOBs

Complexity-Approximation Trade-offs in Exchange Mechanisms: AMMs vs. LOBs

Invoice Discounting Using Kelly Criterion by Automated Market Makers-like Implementations

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