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Concentrated Liquidity Market Makers (CLMMs) represent a fundamental innovation in market microstructure, transforming liquidity provision from passive portfolio allocation to active risk management. This evolution creates significant…
In this paper we derive a second order approximation for an infinite dimensional limit order book model, in which the dynamics of the incoming order flow is allowed to depend on the current market price as well as on a volume indicator…
A new method for stochastic control based on neural networks and using randomisation of discrete random variables is proposed and applied to optimal stopping time problems. The method models directly the policy and does not need the…
In this paper we provide a complete theoretical analysis of a two-dimensional degenerate non convex singular stochastic control problem. The optimisation is motivated by a storage-consumption model in an electricity market, and features a…
We consider a dynamic pricing problem in network revenue management where customer behavior is predicted by a choice model, i.e., the multinomial logit (MNL) model. The problem, even in the static setting (i.e., customer demand remains…
We study the relaxation dynamics of the bid-ask spread and of the midprice after a sudden, large variation of the spread, corresponding to a temporary crisis of liquidity in a double auction financial market. We find that the spread decays…
In this paper, a linear second order numerical scheme is developed and investigated for the Allen-Cahn equation with a general positive mobility. In particular, our fully discrete scheme is mainly constructed based on the Crank-Nicolson…
In this article we discuss the problem of calculating optimal model-independent (robust) bounds for the price of Asian options with discrete and continuous averaging. We will give geometric characterisations of the maximising and the…
Automated market makers (AMMs) are smart contracts that automatically trade electronic assets according to a mathematical formula. This paper investigates how an AMM's formula affects the interests of liquidity providers, who endow the AMM…
This paper investigates optimal execution strategies in intraday energy markets through a mutually exciting Hawkes process model. Calibrated to data from the German intraday electricity market, the model effectively captures key empirical…
In this paper we study a general optimal liquidation problem with a control-dependent stopping time which is the first time the stock holding becomes zero or a fixed terminal time, whichever comes first. We prove a stochastic maximum…
A first attempt at obtaining market--directional information from a non--stationary solution of the dynamic equation "future price tends to the value that maximizes the number of shares traded per unit time" [1] is presented. We demonstrate…
Automated Market Makers (AMMs) are a central component of decentralized exchanges, yet their equilibrium foundations and microeconomic mechanisms remain incompletely understood. This paper develops a dynamic equilibrium framework for…
Impacts of liquid droplets on wind turbine blade surfaces, for example sea sprays, can result in material damage through erosion. In this study, we derive an explicit, closed-form analytical approximation for droplet impact and subsequent…
Liquidity Providers on Automated Market Makers generate millions of USD in transaction fees daily. However, the net value of a Liquidity Position is vulnerable to price changes in the underlying assets in the pool. The dominant measure of…
In this paper, we simulate the execution of a large stock order with real data and general power law in the Almgren and Chriss model. The example that we consider is the liquidation of a large position executed over the course of a single…
Model Predictive Control (MPC) is widely used to achieve performance objectives, while enforcing operational and safety constraints. Despite its high performance, MPC often demands significant computational resources, making it challenging…
We introduce methods for large scale Brownian Dynamics (BD) simulation of many rigid particles of arbitrary shape suspended in a fluctuating fluid. Our method adds Brownian motion to the rigid multiblob method at a cost comparable to the…
Empirical scaling laws prescribe how to allocate parameters, data, and compute, while maximal-update parameterization ($\mu$P) enables learning-rate transfer across widths by equalizing early-time update magnitudes. However, in modern…
There is growing interest in the use of grid-level storage to smooth variations in supply that are likely to arise with increased use of wind and solar energy. Energy arbitrage, the process of buying, storing, and selling electricity to…