A locally-built, LLM-digested index of recent arXiv papers in quant finance, geometry/topology, and statistical ML — keyword search served straight from SQLite on this machine.
Study analyzes a new algorithm for complex optimization problems.
A new approach models exploration in continuous-time RL using random measures.
Continuous time random walks impose a random waiting time before each particle jump. Scaling limits of heavy tailed continuous time random walks are governed by fractional evolution equations. Space-fractional derivatives describe heavy tailed jumps, and the time-fractional version codes heavy tailed waiting times. Thi…
Stochastic gradient descent in continuous time (SGDCT) provides a computationally efficient method for the statistical learning of continuous-time models, which are widely used in science, engineering, and finance. The SGDCT algorithm follows a (noisy) descent direction along a continuous stream of data. The parameter …
New SDE model for continuous-time reinforcement learning.
Study high-frequency trading game with price impact, finding unique equilibrium.
Accelerated gradient methods play a central role in optimization, achieving optimal rates in many settings. While many generalizations and extensions of Nesterov's original acceleration method have been proposed, it is not yet clear what is the natural scope of the acceleration concept. In this paper, we study accelera…
In this paper, a finite-state mean-reverting model for the short-rate, based on the continuous time Ehrenfest process, will be examined. Two explicit pricing formulae for zero-coupon bonds will be derived in the general and the special symmetric cases. Its limiting relationship to the Vasicek model will be examined wit…
We aim to construct the optimal solutions to the undiscounted continuous-time infinite horizon optimization problems, the objective functionals of which may be unbounded. We identify the condition under which the limit of the solutions to the finite horizon problems is optimal for the infinite horizon problems under th…
Graph neural networks learn PDEs from sparse, irregular data.
We derive the ODE of MAML and propose a new BI-MAML algorithm.
New methods for calculating curvature in graph theory.
The discrete-time GARCH methodology which has had such a profound influence on the modelling of heteroscedasticity in time series is intuitively well motivated in capturing many `stylized facts' concerning financial series, and is now almost routinely used in a wide range of situations, often including some where the d…
Improved continuous-time consistency models for large-scale image generation.
New method decomposes profits and losses continuously, avoiding discrete reporting issues.
Proposes a new algorithm for learning continuous-time Bayesian network structures.
The paper studies problem of continuous time optimal portfolio selection for a incom- plete market diffusion model. It is shown that, under some mild conditions, near optimal strategies for investors with different performance criteria can be constructed using a limited number of fixed processes (mutual funds), for a m…
Naive investors make riskier choices than optimal strategies in continuous-time finance.
In this paper we consider long-run risk sensitive average cost impulse control applied to a continuous-time Feller-Markov process. Using the probabilistic approach, we show how to get a solution to a suitable continuous-time Bellman equation and link it with the impulse control problem. The optimal strategy for the und…
In this paper we propose the notion of continuous-time dynamic spectral risk-measure (DSR). Adopting a Poisson random measure setting, we define this class of dynamic coherent risk-measures in terms of certain backward stochastic differential equations. By establishing a functional limit theorem, we show that DSRs may …
We derive a continuous time model for the joint evolution of the mid price and the bid-ask spread from a multiscale analysis of the whole limit order book (LOB) dynamics. We model the LOB as a multiclass queueing system and perform our asymptotic analysis using stylized features observed empirically. We argue that in t…
High Frequency Trading (HFT) represents an ever growing proportion of all financial transactions as most markets have now switched to electronic order book systems. The main goal of the paper is to propose continuous time equations which generalize the self-financing relationships of frictionless markets to electronic …
In this paper we study a continuous time equilibrium model of limit order book (LOB) in which the liquidity dynamics follows a non-local, reflected mean-field stochastic differential equation (SDE) with evolving intensity. Generalizing the basic idea of Ma et al. (2015), we argue that the frontier of the LOB (e.g., the…
We consider the problem of estimating the transition rate matrix of a continuous-time Markov chain from a finite-duration realisation of this process. We approach this problem in an imprecise probabilistic framework, using a set of prior distributions on the unknown transition rate matrix. The resulting estimator is a …
We derive formulas for the performance of capital assets in continuous time from an efficient market hypothesis, with no stochastic assumptions and no assumptions about the beliefs or preferences of investors. Our efficient market hypothesis says that a speculator with limited means cannot beat a particular index by a …
We study an optimal execution problem with uncertain market impact to derive a more realistic market model. We construct a discrete-time model as a value function for optimal execution. Market impact is formulated as the product of a deterministic part increasing with execution volume and a positive stochastic noise pa…
We study the high-frequency limits of strategies and costs in a Nash equilibrium for two agents that are competing to minimize liquidation costs in a discrete-time market impact model with exponentially decaying price impact and quadratic transaction costs of size . We show that, for , equilibrium strategie…
Enhances RL for jump processes using MSBVE algorithm.
Continuous-time optimal stopping solved with deep reinforcement learning
Paper solves Bayesian bandit problem with continuous-time limit and approximate policy.
ADD-THIN improves TPP forecasting by handling long-term data sequences.
It is well known that mean-variance portfolio selection is a time-inconsistent optimal control problem in the sense that it does not satisfy Bellman's optimality principle and therefore the usual dynamic programming approach fails. We develop a time- consistent formulation of this problem, which is based on a local not…
Gradient descent-based optimization methods underpin the parameter training of neural networks, and hence comprise a significant component in the impressive test results found in a number of applications. Introducing stochasticity is key to their success in practical problems, and there is some understanding of the rol…
Stochastic gradient descent (SGD) has been widely used in machine learning due to its computational efficiency and favorable generalization properties. Recently, it has been empirically demonstrated that the gradient noise in several deep learning settings admits a non-Gaussian, heavy-tailed behavior. This suggests tha…
Continuous time random walks (CTRWs) are used in physics to model anomalous diffusion, by incorporating a random waiting time between particle jumps. In finance, the particle jumps are log-returns and the waiting times measure delay between transactions. These two random variables (log-return and waiting time) are typi…
New method uses differential equations for better counterfactual analysis.
Study approximates financial market with discrete-time models.
We analyze a tractable model of a limit order book on short time scales, where the dynamics are driven by stochastic fluctuations between supply and demand. We establish the existence of a limiting distribution for the highest bid, and for the lowest ask, where the limiting distributions are confined between two thresh…
New method resolves time order in genetic mutation models.
Paper introduces efficient methods for probabilistic querying of event sequences.
Faster policy learning via continuous-time gradients.
Deep-MacroFin uses neural networks to solve complex economic models efficiently.
Continuous time framework for discrete data denoising models.
New method learns policies from offline data using operator models.
We prove limit theorems for the super-replication cost of European options in a Binomial model with friction. The examples covered are markets with proportional transaction costs and the illiquid markets. The dual representation for the super-replication cost in these models are obtained and used to prove the limit the…
Unified analysis of stochastic ADMM variants via SME.
The paper studies market viability and completeness in discrete markets.
We study the optimal execution of market and limit orders with permanent and temporary price impacts as well as uncertainty in the filling of limit orders. Our continuous-time model incorporates a trade speed limiter and a trader director to provide better control on the trading rates. We formulate a stochastic control…