Investors face reduced risk and performance loss under dynamic risk constraints in continuous vs. discrete trading.
problem Optimizing portfolio under dynamic risk constraints in continuous and discrete time trading.
method Derive dynamic programming equations for stochastic optimal control problems and solve numerically.
result Loss of expected utility due to dynamic risk constraints is significant but manageable.
Study of electronic corn futures trading shows discrete price changes and non-Gaussian distributions.
problem Discrepancy between theoretical continuous price models and actual intra-day trading data.
method Analysis of discrete price increments, volume, and profit strategies using statistical distributions and probability theory.
result Kumaraswamy distribution better fits waiting times than Weibull, and price jumps resemble branching reactions.
Kernel interpolation improved with continuous volume sampling.
problem Approximating functions from RKHS using weighted sums of kernel translates.
method Continuous volume sampling for choosing node locations.
result Proved almost optimal bounds for interpolation and quadrature under VS.
Study compares static vs adaptive strategies in two trading models.
problem Optimal execution in static vs adaptive strategies.
method Discrete and continuous time models with permanent and temporary impact.
result Static strategies are nearly as optimal as adaptive ones in the studied models.
Study shows financial value of weak information converges in discrete vs continuous markets.
problem Analyzing financial value of weak information in discrete vs continuous markets.
method Defined minimal probability measure and financial value of weak information, then showed convergence.
result Financial value of weak information converges in discrete vs continuous markets.
Earth observation embeddings can convert discrete biome maps into continuous representations that better capture ecological variation.
problem Biome maps impose categorical boundaries that compress continuous variation in biotic communities.
method Fit a linear classifier on Earth observation embeddings to predict biome labels.
result Continuous biome representation outperforms discrete biome labels for predicting species occurrence.
Neural networks learn discrete tasks on continuous data via emergent geometry.
problem Understanding how neural networks perform discrete computations on continuous data.
method Analysis of Riemannian pullback metric across neural network layers.
result Neural networks learn to discretize continuous inputs and perform logical operations on these discretized variables.
In the present paper we construct stock price processes with the same marginal log-normal law as that of a geometric Brownian motion and also with the same transition density (and returns' distributions) between any two instants in a given discrete-time grid. We then illustrate how option prices based on such processes…
This research explores discrete diffusion models for natural language generation.
problem Challenges in applying diffusion models to discrete data, especially natural language.
method Investigates Discrete Denoising Diffusion Probabilistic Model (D3PM) and compares it with autoregressive models.
result Discrete diffusion models achieve better processing speed than autoregressive models.
Hybrid RL method optimizes trading by balancing continuous and discrete actions.
problem Optimal execution in algorithmic trading with continuous-discrete action space.
method Combines continuous and discrete RL agents for better trading decisions.
result Significantly outperforms existing methods in trading efficiency and stability.
Achilles predicts Gold vs USD with a profitable trading bot.
problem Accurate and consistent prediction of commodity prices.
method LSTM neural network for minute-by-minute predictions.
result $1623.52 profit in 23 days of testing.
Paper tackles P vs NP problem in portfolio optimization with cardinality constraints and Black-Scholes derivatives.
problem Operationalizing the P vs NP problem in cardinality-constrained portfolio selection.
method Mixed-integer quadratic program with genetic algorithms, Monte Carlo sampling, and greedy screening.
result Cardinality constraint reshapes efficient frontier, highlighting trade-offs between stability and computational cost.
Study high-frequency trading game with price impact, finding unique equilibrium.
problem Optimal execution in a trading game with transient price impact.
method Analyzes high-frequency limit of an n-trader optimal execution game. result High-frequency limit converges to a continuous-time model with quadratic costs.
Foundation models fail to preserve continuous geometry, identified as the Geometric Alignment Tax.
problem Continuous geometry is lost in foundation models due to discrete categorical bottlenecks.
method Controlled ablations on synthetic systems and evaluation of 14 biological models using rate-distortion theory and MINE.
result Replacing cross-entropy with a continuous head reduces geometric distortion by up to 8.5x.
New insights into RL efficiency from managing time discretization.
problem The impact of time discretization on RL methods in continuous-time systems.
method Analysis of Monte-Carlo policy evaluation for LQR systems.
result An optimal choice of temporal resolution for a given data budget improves policy evaluation efficiency.
We introduce a new formulation of asset trading games in continuous time in the framework of the game-theoretic probability established by Shafer and Vovk (Probability and Finance: It's Only a Game! (2001) Wiley). In our formulation, the market moves continuously, but an investor trades in discrete times, which can dep…
New insights into neural network forgetting reveal a trade-off between node activation and re-use.
problem Challenges in maintaining performance on old tasks while learning new ones.
method Theoretical analysis of synthetic and real data setups, focusing on node activation vs re-use.
result Worst forgetting occurs in an intermediate similarity regime between learned tasks.
We develop a polynomial method to optimize trading in markets with transaction costs.
problem Optimizing trading strategies in markets with proportional transaction costs.
method Polynomial approximation of the residual value function to determine optimal trading strategies.
result Identify the trade-off between trading frequency and trade sizes for satisfactory agreement with theoretically optimal strategies.
Investment strategy optimization from discrete to continuous models.
problem Optimizing investment strategies and stopping times in both continuous and discrete settings.
method Characterized value functions via quadratic reflected BSDEs for continuous case, discretized BSDEs for discrete case, and derived uniform convergence rates.
result Uniform convergence and rate from discrete to continuous quadratic reflected BSDEs.
We consider the pricing of derivatives in a setting with trading restrictions, but without any probabilistic assumptions on the underlying model, in discrete and continuous time. In particular, we assume that European put or call options are traded at certain maturities, and the forward price implied by these option pr…
High-frequency traders can act as either small informed traders or round-trippers, affecting price discovery and liquidity.
problem Effects of high-frequency trading on price discovery and liquidity.
method Extended Kyle's model with interactions between large informed traders and high-frequency traders.
result High-frequency traders can act as Small-IT or Round-Tripper, impacting price discovery and liquidity.
CADD improves generative quality by augmenting discrete diffusion with continuous latent space.
problem Loss of semantic information between denoising steps in discrete diffusion models.
method Introduces a framework that augments discrete state space with a continuous latent space, allowing for graded, informative masked tokens.
result CADD improves generative quality across text generation, image synthesis, and code modeling.
Investigates trading with integer constraints in discrete time.
problem Trading with discrete, integer quantities under integer constraints.
method Establishes a novel theory of integer arbitrage-free pricing and hedging for non-rational price processes.
result The set of prices of a contingent claim is either empty or dense in an interval.
This paper proposes a continuous timing strategy for growth vs. defensive style allocation.
problem Dynamic allocation of growth and defensive ETF baskets using macro-market timing signals.
method Continuous smooth score combining multiple factors, mapped to G/D weights, smoothed with EWMA.
result Continuous style timing strategy outperforms static benchmarks in risk-adjusted returns.
Dynamic-weight AMMs outperform traditional CEX rebalancing in tokenized funds, especially on L2s.
problem Improving asset allocation efficiency in decentralized finance (DeFi) protocols.
method Block-level arbitrage analysis and long-term performance benchmarks on two live pools.
result Dynamic-weight AMMs can achieve performance comparable to or better than traditional CEX rebalancing, especially on Layer 2 (L2) networks.
Method reveals multi-timescale trading dynamics in online financial markets.
problem Capturing and characterizing trading dynamics at different time scales.
method Non-negative tensor factorization (NTF) for multi-timescale activity patterns.
result NTF uncovers hidden activity patterns and crisis modalities in trading.
Complex contagion model explains financial fire sales through continuous asset prices.
problem Modeling financial fire sales with a continuum of asset prices.
method Developed a threshold model of continuous-state cascades using real values for asset prices.
result Discretization approach accurately replicates the distribution of defaulted banks and asset prices.
We study a problem of optimal investment/consumption over an infinite horizon in a market consisting of a liquid and an illiquid asset. The liquid asset is observed and can be traded continuously, while the illiquid one can only be traded and observed at discrete random times corresponding to the jumps of a Poisson pro…
New findings show sampling vs optimization are incomparable in non-convex cases.
problem Comparing sampling and optimization in non-convex Bayesian learning.
method Simpler and stronger separation of sampling and optimization.
result Provable incomparability of sampling and optimization in non-convex cases.
Deep reinforcement learning boosts commodities trading performance.
problem Improving algorithmic trading performance in commodities markets.
method Formulated as a stochastic dynamical system, employed actor-based and actor-critic-based policy gradient algorithms with CNN and LSTM function approximators.
result DRL models increase Sharpe ratio by 83% compared to buy-and-hold.
Study evaluates discretized arbitrage strategies in fractional financial markets.
problem Serial correlation in financial markets with fractional Brownian motion.
method Revisit and transfer Shiryaev and Salopek's strategies to a real-world setting, distretizing dynamics and introducing transaction costs.
result Both strategies are promising with respect to terminal portfolio values and loss probabilities.
This paper compares two methods for training neural ODEs in time-series regression and CNFs.
problem Training neural ODEs for time-series regression and CNFs efficiently.
method Discretize-Optimize (Disc-Opt) vs. Optimize-Discretize (Opt-Disc) approaches.
result Disc-Opt methods can achieve similar performance as Opt-Disc at inference with drastically reduced training costs.
Deep RL strategies outperform classical models in trading.
problem Designing profitable trading strategies for futures contracts.
method Deep Reinforcement Learning with volatility scaling.
result Deep RL algorithms outperformed classical models with positive profits.
In this work, we consider the hedging error due to discrete trading in models with jumps. Extending an approach developed by Fukasawa [In Stochastic Analysis with Financial Applications (2011) 331-346 Birkhäuser/Springer Basel AG] for continuous processes, we propose a framework enabling us to (asymptotically) optimize…
This paper proposes a trading strategy using TD3 for stock and cryptocurrency markets.
problem Predicting price movements in financial markets using historical data.
method Twin-Delayed DDPG (TD3) for continuous action space in algorithmic trading.
result The proposed strategy improves trading performance based on Return and Sharpe ratio metrics.
We price and hedge American options robustly in continuous time.
problem Pricing and hedging American options in continuous time with model uncertainty.
method Assumes continuous semimartingale asset prices and closed convex constraints on volatility. Proves robust pricing-hedging duality and identifies American options as European options on an enlarged space.
result We prove robust pricing-hedging duality and show it holds against richer models with dynamic trading of European options.
We study a problem of optimal investment/consumption over an infinite horizon in a market consisting of two possibly correlated assets: one liquid and one illiquid. The liquid asset is observed and can be traded continuously, while the illiquid one can be traded only at discrete random times corresponding to the jumps …
We study the problem of optimal portfolio selection in an illiquid market with discrete order flow. In this market, bids and offers are not available at any time but trading occurs more frequently near a terminal horizon. The investor can observe and trade the risky asset only at exogenous random times corresponding to…
Study proves existence and convergence of discrete-time Kyle models with multiple insiders.
problem Existence and convergence of discrete-time Kyle models with multiple informed traders.
method Proves existence and convergence of discrete-time Kyle models with multiple informed traders using mathematical proofs.
result Equilibrium exists and converges to continuous-time equilibrium as the number of trading times increases.
A new discrete privacy mechanism for federated learning.
problem Differentially private federated learning with communication constraints.
method Skellam mechanism based on Poisson distributions.
result Skellam mechanism provides similar privacy-accuracy trade-offs as Gaussian mechanism.
Extends option pricing model to incorporate market factor dynamics.
problem Option pricing models need to account for market influencing factors.
method Extended Kim-Stoyanov-Rachev-Fabozzi model using invariance principles.
result New binomial model for complete markets with log-return dynamics.
Private two-sample tests under LDP achieve minimax rates for multinomial and continuous data.
problem Achieving statistical utility while maintaining privacy in two-sample testing.
method Private permutation tests for multinomial data and adaptive tests for continuous data.
result Minimax optimal tests for private two-sample testing under LDP.
High-frequency traders manage inventories to exploit price information, leading to mean-reverting inventories and excess trading.
problem Managing inventories for high-frequency traders in imperfect competition.
method Analyzes Nash equilibria for inventory-averse HFTs using nonlinear equations and asymptotic analysis.
result Optimal inventories become mean-reverting and vanish in the continuous-time limit, while HFTs' profits converge to risk-neutral counterparts.
In our simplified description `wealth' is money (m). A kinetic theory of gas like model of money is investigated where two agents interact (trade) selectively and exchange some amount of money between them so that sum of their money is unchanged and thus total money of all the agents remains conserved. The probabilit…
GEM-T generates synthetic tabular data by fitting moments, outperforming neural networks.
problem Generating synthetic tabular data from limited or sensitive real-world data.
method Generative Entropy Maximization (MaxEnt) for tables, capturing nth-order interactions.
result GEM-T matches or exceeds deep neural network approaches in 23 out of 34 datasets.
Players choose rebalancing rules to maximize their wealth relative to others in a continuous-time trading game.
problem Optimizing wealth in a continuous-time trading game between two players.
method Players choose rebalancing rules to maximize their expected wealth ratio, using the Kelly rule in equilibrium.
result The Kelly rule emerges as the optimal strategy in both short and long time intervals.
We introduce a prototype model in an attempt to capture some aspects of market dynamics simulating a trading mechanism. The model description starts with a discrete-space, continuous-time Markov process describing arrival and movement of orders with different prices. We then perform a re-scaling procedure leading to a …
Extends FTAP to large financial markets with two filtrations.
problem Modeling asset pricing in complex financial markets.
method Generalizes FTAP to continuous time, large markets with two filtrations, without assuming specific properties of price processes.
result A simplified version of FTAP for large financial markets with two filtrations.