We find a simple strategy approximating optimal portfolio for short time horizons.
problem Optimizing portfolios in incomplete markets with general utility functions.
method Closed-form formula derived from HJB PDE, approximated by sub- and super-solutions.
result Approximation formula for optimal trading strategy is accurate for small time horizons.
Short-horizon bias causes meta-optimization to favor small learning rates.
problem Short-horizon bias in meta-optimization leads to suboptimal learning rates.
method Analyzes a noisy quadratic cost function and runs meta-optimization experiments on benchmark datasets.
result Meta-optimization chooses too small a learning rate, even with a long time horizon.
Optimizes investment under uncertain time horizons with non-concave utility.
problem Optimizing investment decisions with non-concave utility and uncertain time horizons.
method Established necessary and sufficient conditions for optimality, suggested recursive procedure for non-concave utility.
result Optimal investment strategies under uncertain time horizons exhibit multimodal distribution, indicating flexibility in switching between local maximizers.
Developed LQ MFG theory with common noise, proving existence and uniqueness.
problem Linear-quadratic mean field games with common noise.
method Coupled forward-backward stochastic evolution equations (FBSEEs) in Hilbert spaces.
result Existence and uniqueness of solutions for small and arbitrary finite time horizons.
We study existence and uniqueness of continuous-time stochastic Radner equilibria in an incomplete market model among a group of agents whose preference is characterized by cash invariant time-consistent monetary utilities. An assumption of "smallness" type is shown to be sufficient for existence and uniqueness. In par…
Langevin dynamics fails to produce accurate samples even with small score function errors.
problem Robustness of Langevin dynamics to score function errors.
method Analysis of Langevin dynamics and score function errors.
result Langevin dynamics produces a distribution far from the target distribution in TV distance even with small L2 errors in the score function. New neural network learns seismic horizon locations from few images.
problem Automated detection of seismic horizons from small patches is inefficient.
method Multi-resolution U-net with projected loss-function for non-linear regression.
result Network accurately predicts horizon locations even far from known areas.
Optimizes portfolio in volatile markets with jumps, providing accurate formulas.
problem Optimizing wealth in a volatile financial market with jumps.
method Analyzes an incomplete stochastic volatility model, derives closed-form portfolio formulas using HJB equation and super-solution/sub-solution.
result Proves accuracy of derived portfolio formulas for both small and finite time horizons.
In a market with one safe and one risky asset, an investor with a long horizon, constant investment opportunities, and constant relative risk aversion trades with small proportional transaction costs. We derive explicit formulas for the optimal investment policy, its implied welfare, liquidity premium, and trading volu…
A large class of vacuum space-times is constructed in dimension 4+1 from hyperboloidal initial data sets which are not small perturbations of empty space data. These space-times are future geodesically complete, smooth up to their future null infinity, and extend as vacuum space-times through their Cauchy horizon. Dime…
The paper optimizes portfolios in a financial market with correlated assets using a stochastic volatility model.
problem Optimizing portfolios in a financial market with correlated assets and stochastic volatility.
method Derive a Hamilton-Jacobi-Bellman equation, use approximation methods, analyze value function using expansion of utility function, control error with second-order terms, generate close-to-optimal portfolio.
result Close-to-optimal portfolio generated using first-order approximation of utility function with controlled error.
Proves uniqueness of non-extremal Kerr-Newman black holes under small perturbations.
problem Uniqueness of non-extremal Kerr-Newman black holes under small perturbations.
method Perturbative analysis using Mars-Simon type tensors.
result Proves that a space-time close to the Kerr-Newman family must be one of the Kerr-Newman solutions.
We extend and test empirically the multifractal model of asset returns based on a multiplicative cascade of volatilities from large to small time scales. The multifractal description of asset fluctuations is generalized into a multivariate framework to account simultaneously for correlations across times scales and bet…
New control theory shows neural networks can be sparsely active over time.
problem Optimizing neural networks for long-time control with sparsity constraints.
method Proving optimal controls vanish after a positive time and providing a stability estimate.
result Optimal controls for ℓ1-penalized neural ODEs are sparsely active over time. Study optimal stock order placement in a diffusive market.
problem Optimal placement of a small order in a diffusive limit order book.
method Characterization of optimal limit order placement policy, analysis of behavior under different market conditions, and a simple method to approximate critical time and optimal order placement.
result Existence of a critical time t0 such that for t > t0, optimal placement differs from the best bid and second best bid.
New model improves equity derivative pricing accuracy.
problem Inaccurate pricing of equity derivatives.
method Introduces Additive Normal Tempered Stable process.
result Calibration yields better results than existing methods.
We analyze the horizon and geodesic structure of a class of 4D off--diagonal metrics with deformed spherical symmetries, which are exact solutions of the vacuum Einstein equations with anholonomic variables. The maximal analytic extension of the ellipsoid type metrics are constructed and the Penrose diagrams are analyz…
New algorithms reduce contextual bandits' regret without knowing reward noise variances.
problem Reducing regret in contextual bandits with unknown reward noise variances.
method Developed new algorithms based on the optimism principle.
result Regret scales as the square root of the sum of measurement variances, not the time horizon.
Study shows formation of Kerr black holes with complete apparent horizons and proves Penrose inequalities.
problem Formation of Kerr black holes and Penrose inequalities.
method Combining gravitational-collapse and Kerr stability results with new coordinate changes and elliptic arguments.
result Proves dynamical and spacetime Penrose inequalities in black hole formation spacetimes.
ElasTST improves time-series forecasting across varying horizons.
problem Robust forecasting across different time horizons in varied industrial sectors.
method Elastic Time-Series Transformer (ElasTST) with non-autoregressive design, rotary position embedding, and multi-scale patching.
result ElasTST provides robust forecasts across varying horizons without retraining.
The paper proposes confidence horizons for anytime-valid inference with finite time constraints.
problem The need for stopping experiments early with valid inference under finite time horizons.
method Confidence horizons as large-sample confidence sequences or group sequential repeated confidence intervals.
result It is possible to obtain sharper large-sample anytime-valid inference by forgoing validity beyond a finite time horizon.
We study constant mean curvature Lorentzian hypersurfaces of R1,d+1 from the point of view of its Cauchy problem. We completely classify the spherically symmetric solutions, which include among them a manifold isometric to the de Sitter space of general relativity. We show that the spherically symmetric s…
This paper studies the utility maximization problem with changing time horizons in the incomplete Brownian setting. We first show that the primal value function and the optimal terminal wealth are continuous with respect to the time horizon T. Secondly, we exemplify that the expected utility stemming from applying th…
TD-Flow improves long-term predictions in agent learning.
problem Cumulative errors in step-by-step inference of future states.
method Leverages flow-matching techniques and a novel Bellman equation to learn accurate geometric horizon models.
result Significantly reduces errors at long horizons compared to prior methods.
We consider the problem of optimizing the expected logarithmic utility of the value of a portfolio in a binomial model with proportional transaction costs with a long time horizon. By duality methods, we can find expressions for the boundaries of the no-trade-region and the asymptotic optimal growth rate, which can be …
The paper finds the shortest time to exploit arbitrage in multi-stock markets.
problem Finding the shortest time to exploit arbitrage in multi-stock markets.
method Characterizes the minimal time horizon for relative arbitrage in markets with 2 to 3 stocks and uses geometric flows for markets with 4 or more stocks.
result Explicit computation of minimal time horizon for 2 and 3 stocks markets, and characterization via geometric flows for markets with 4 or more stocks.
Uniqueness theorem for extremal charged black holes in de Sitter space.
problem Proving uniqueness of extremal charged black holes in de Sitter space.
method Analyzing Einstein-Maxwell theory with a positive cosmological constant.
result Local isometry to extremal Reissner-Nordström-de Sitter black hole or its near-horizon geometry.
Unified pipeline predicts equipment anomalies with high precision and reduced false positives.
problem Predicting equipment anomalies before failures using small models.
method Triplet Feature Fusion combining statistical, time-series, and text embeddings.
result Achieves high precision and reduced false positives.
In this paper, we construct a family of asymptotically hyperbolic manifolds with horizons and with scalar curvature equal to -6. The manifolds we constructed can be arbitrary close to anti-de Sitter-Schwarzschild manifolds at infinity. Hence, the mass of our manifolds can be very large or very small. The main arguments…
Study on BSDEs with random time horizon, focusing on existence and properties.
problem Existence of solutions to BSDEs and reflected BSDEs with a random time horizon.
method Method of reduction and examination of BSDEs with lahdlaug driver.
result Existence of solutions to BSDEs and reflected BSDEs with a random time horizon.
Study how learning impacts decision-making in project expansion.
problem Optimal timing of expansion decisions based on uncertain project profitability.
method Bayesian updating model with two irreversible alternatives (exit or expansion).
result Time-to-decision is not monotonic with information arrival rate.
Unified RNN architecture improves multi-time-horizon solar forecasting.
problem Large prediction errors in traditional solar forecasting methods.
method Recurrent Neural Network (RNN) for multi-time-horizon solar forecasting.
result Lower root-mean-squared prediction error compared to previous methods.
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…
Model predicts parking area states up to 60 mins ahead.
problem Predicting parking area states for urban traffic management.
method Neural Network-based model using real-time and historic data.
result Model outperforms naive models by over 150% at 60 mins prediction.
Optimized portfolio turnover strategies enhance wealth and reduce costs.
problem Minimizing transaction costs and maximizing wealth in small to medium-sized portfolios.
method Dynamic multi-period model with column generation algorithm to minimize turnover constraints.
result The proposed model leads to higher portfolio values and lower transaction costs compared to a naive model.
Using black-hole inequalities and the increase of the horizon's areas, we show that there are arbitrarily small electro-vacuum perturbations of the standard initial data of the extreme Reissner-Nordstrom black-hole that, (by contradiction), cannot decay in time into any extreme Kerr-Newman black-hole. This proves the e…
Foundation models improve on econometric benchmarks for forecasting volatility, but vary widely across models.
problem Comparing pretrained time series foundation models to econometric benchmarks for volatility forecasting.
method Systematic comparison of nine zero-shot TSFMs against eight econometric specifications on 50 assets across 3 markets and 3 horizons.
result Tiny Time Mixers (TTM) is the only model that consistently beats the Log-HAR benchmark, but performance varies widely across models.
ForecastGAN improves multi-horizon time series forecasting by integrating numerical and categorical features.
problem Limited performance of existing approaches in short-term and long-term forecasting.
method Decomposition, model selection, adversarial training.
result ForecastGAN consistently outperforms state-of-the-art transformer models for short-term forecasting.
Paper fine-tunes a language model to predict long-term stock buy signals.
problem Predicting long-term stock price movements with narrative text.
method Fine-tuning a small language model on 10-K reports for buy/sell decisions.
result Buy signals generated from 10-K text are most precise at 6 and 9 months, providing 4.8-9% improvement over random selection.
We show that the supersymmetric near horizon black hole geometries of 6-dimensional supergravity coupled to any number of scalar and tensor multiplets are either locally AdS3×Σ3, where Σ^3 is a homology 3-sphere, or $\bR^{1,1}\times {\cal S}^4$, where S4 is a 4-manifold whose geometry depends on the…
The horizon and geodesic structure of static configurations generated by anisotropic conformal transforms of the Schwarzschild metric is analyzed. We construct the maximal analytic extension of such off--diagonal vacuum metrics and conclude that for small deformations there are different classes of vacuum solutions of …
The paper analyzes how sensitive long-term utility of optimal portfolios is to changes in market models.
problem Sensitivity of long-term expected utility of optimal portfolios to market model changes.
method Analyzes utility maximization problem with long-time horizon under incomplete market given by a factor model, focusing on eigenpairs of operators.
result Eigenpairs determine long-term sensitivity of optimal expected utility to market model changes.
For an investor with constant absolute risk aversion and a long horizon, who trades in a market with constant investment opportunities and small proportional transaction costs, we obtain explicitly the optimal investment policy, its implied welfare, liquidity premium, and trading volume. We identify these quantities as…
We investigate the growth optimal strategy over a finite time horizon for a stock and bond portfolio in an analytically solvable multiplicative Markovian market model. We show that the optimal strategy consists in holding the amount of capital invested in stocks within an interval around an ideal optimal investment. Th…
Study optimal portfolios in a non-Markovian regime-switching model with random time horizon.
problem Optimal portfolio selection in a market with non-Markovian regime-switching and random time horizon.
method Formulated as a constrained stochastic linear-quadratic optimal control problem, derived closed-form expressions for optimal portfolios and efficient frontier.
result Closed-form expressions for optimal portfolios and efficient frontier derived under non-Markovian regime-switching and random time horizon.
A correct description of the past and the future event horizons for timelike geodesics in de Sitter space-time of the first kind is given.
Study of isometries in spacetimes without observer horizons.
problem Understanding the symmetries of spacetimes without specific boundaries.
method Analysis of isometry groups in causal spacetimes without observer horizons.
result The group of time orientation-preserving isometries acts properly on the spacetime.
Optimizes dividend payments to balance risk and reward.
problem Maximizing mean-variance of accumulated discounted dividends up to ruin.
method Develops a time-consistent equilibrium strategy using a verification lemma.
result Equilibrium strategy is a barrier strategy for low risk aversion.