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We present the first formal treatment of \emph{yield tokenization}, a mechanism that decomposes yield-bearing assets into principal and yield components to facilitate risk transfer and price discovery in decentralized finance (DeFi). We…
This research presents a comprehensive framework for analyzing liquidity in financial markets, particularly in the context of high-frequency trading. By leveraging advanced machine learning classification techniques, including Logistic…
Financial markets are often modelled as if time were unique and continuous across assets and markets. Financial markets are however asynchronous, order flow is event-driven, and waiting times between events are often random. Many of the…
Automated market makers (AMM) have grown to obtain significant market share within the cryptocurrency ecosystem, resulting in a proliferation of new products pursuing exotic strategies for horizontal differentiation. Yet, their theoretical…
Equations of motion with delays naturally emerge in the analysis of complex biological control systems which are organized around biochemically mediated feedback interactions. We study the properties of a Mackey-Glass-type nonlinear map…
Constant Product Market Makers use fees that are typically fixed proportions of trade size. When these fees are automatically reinvested into the pool, as in Uniswap~V2 and some designs of Uniswap V4, the final state after a trade can…
Mandatory emission trading schemes are being established around the world. Participants of such market schemes are always exposed to risks. This leads to the creation of an accompanying market for emission-linked derivatives. To evaluate…
This work focuses on the mathematical study of constant function market makers. We rigorously establish the conditions for optimal trading under the assumption of a quasilinear, but not necessarily convex (or concave), trade function. This…
This paper introduces a novel theoretical framework and a suite of highly efficient, parallelizable algorithms for solving the large-scale multicommodity flow (MCF) feasibility problem. We reframe the classical constraint-satisfaction…
The paper develops general, discrete, non-probabilistic market models and minmax price bounds leading to price intervals for European options. The approach provides the trajectory based analogue of martingale-like properties as well as a…
We investigate the market microstructure of Automated Market Makers (AMMs), the most prominent type of blockchain-based decentralized exchanges. We show that the order execution mechanism yields token value loss for liquidity providers if…
In this paper we explore optimal liquidation in a market populated by a number of heterogeneous market makers that have limited inventory-carrying and risk-bearing capacity. We derive a reduced form model for the dynamic of their aggregated…
We present a formal framework for the aggregation of financial markets mediated by arbitrage. Our main tool is to characterize markets via utility functions and to employ a one-to-one correspondence to limit order book states. Inspired by…
Continuous diffusion and flow matching models could represent a powerful alternative to autoregressive approaches for language modelling (LM), as they unlock a host of advantages currently reserved for continuous modalities, including…
The classical optimal trading problem is the closure of a position in an asset over a time interval; the trader maximizes an expected utility under the constraint that the position be fully closed by terminal time. Since the asset price is…
This paper investigates the problem of maximizing expected terminal utility in a (generically incomplete) discrete-time financial market model with finite time horizon. In contrast to the standard setting, a possibly non-concave utility…
The current design space of derivatives in Decentralized Finance (DeFi) relies heavily on oracle systems. Replicating market makers (RMMs) provide a mechanism for converting specific payoff functions to an associated Constant Function…
Here, we examine a fully-discrete Semi-Lagrangian scheme for a mean-field game price formation model. We show the existence of the solution of the discretized problem and that it is monotone as a multivalued operator. Moreover, we show that…
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…
This paper formulates a model of utility for a continuous time framework that captures the decision-maker's concern with ambiguity about both volatility and drift. Corresponding extensions of some basic results in asset pricing theory are…