Related papers: A mathematical framework for modelling CLMM dynami…
We consider a discrete-time financial market model with finite time horizon and give conditions which guarantee the existence of an optimal strategy for the problem of maximizing expected terminal utility. Equivalent martingale measures are…
We consider a market where a finite number of players trade an asset whose supply is a stochastic process. The price formation problem consists of finding a price process that ensures that when agents act optimally to minimize their trading…
This whitepaper introduces an innovative mechanism for pricing perpetual contracts and quoting fees to traders based on current market conditions. The approach employs liquidity curves and on-chain oracles to establish a new adaptive…
We study the dynamic pricing of discrete goods over a finite selling horizon. One way to capture both the elastic and stochastic reaction of purchases to price is through a model where sellers control the intensity of a counting process,…
A mathematical framework for Continuous Time Finance based on operator algebraic methods offers a new direct and entirely constructive perspective on the field and leads to new numerical analysis techniques. This is partly a review paper as…
Constant function market makers (CFMMs) are the most popular type of decentralized trading venue for cryptocurrency tokens. In this paper, we give a very general geometric framework (or 'axioms') which encompass and generalize many of the…
In this paper we introduce a completely continuous and time-variate model of the evolution of market limit orders based on the existence, uniqueness, and regularity of the solutions to a type of stochastic partial differential equations…
Automated market makers with concentrated liquidity capabilities are programmable at the tick level. The maximization of earned fees, plus depreciated reserves, is a convex optimization problem whose vector solution gives the best provision…
Recent deployments of large language models (LLMs) as autonomous trading agents raise questions about whether financial decision-making competence generalizes beyond specific market patterns and how it should be trained and evaluated in…
We propose a heterogeneous agent market model (HAM) in continuous time. The market is populated by fundamental traders and chartists, who both use simple linear trading rules. Most of the related literature explores stability, price…
We present a general framework for modelling the dynamics of limit order books, built on the combination of two modelling ingredients: the order flow, modelled as a general spatial point process, and market clearing, modelled via a…
We postulates, and then show experimentally, that liquidity deficit is the driving force of the markets. In the first part of the paper a kinematic of liquidity deficit is developed. The calculus-like approach, which is based on…
In an incomplete financial market, the axiomatic of Time Consistent Pricing Procedure (TCPP), recently introduced, is used to assign to any financial asset a dynamic limit order book, taking into account both the dynamics of basic assets…
Automated Market Makers (AMMs) are major centers of matching liquidity supply and demand in Decentralized Finance. Their functioning relies primarily on the presence of liquidity providers (LPs) incentivized to invest their assets into a…
Assuming that the price in a Uniswap v3 style Automated Market Maker (AMM) follows a Geometric Brownian Motion (GBM), we prove that the strategy that adjusts the position of liquidity to track the current price leads to a deterministic and…
Post Modigliani and Miller (1958), the concept of usage of arbitrage created a permanent mark on the discourses of financial framework. The arbitrage process is largely based on information dissemination amongst the stakeholders operating…
Latency (i.e., time delay) in electronic markets affects the efficacy of liquidity taking strategies. During the time liquidity takers process information and send marketable limit orders (MLOs) to the exchange, the limit order book (LOB)…
We assume a continuous-time price impact model similar to Almgren-Chriss but with the added assumption that the price impact parameters are stochastic processes modeled as correlated scalar Markov diffusions. In this setting, we develop…
In this paper we formulate the now classical problem of optimal liquidation (or optimal trading) inside a Mean Field Game (MFG). This is a noticeable change since usually mathematical frameworks focus on one large trader in front of a…
Here, we study machine learning (ML) architectures to solve a mean-field games (MFGs) system arising in price formation models. We formulate a training process that relies on a min-max characterization of the optimal control and price…