arXiv research

The paper finds the shortest time to exploit arbitrage in multi-stock markets.

The paper studies the question of whether the classical mirror and synchronous couplings of two Brownian motions minimise and maximise, respectively, the coupling time of the corresponding geometric Brownian motions. We establish a characterisation of the optimality of the two couplings over any finite time horizon and…

We first show that the intrinsic, geometrical structure of a dynamical horizon is unique. A number of physically interesting constraints are then established on the location of trapped and marginally trapped surfaces in the vicinity of any dynamical horizon. These restrictions are used to prove several uniqueness theor…

TD-Flow improves long-term predictions in agent learning.

Paper proves existence of anisotropic dynamical horizons in gravitational collapse.

New bounds for prediction with experts using geometric stopping.

The paper proves a geometric capacitary inequality for sub-static manifolds with harmonic potentials.

This is the written version of my talk at SUSY '98. It presents a geometric characterisation of the allowed near-horizon geometries of supersymmetric branes. We focus primarily on the M2-brane, but results for other branes (e.g., the D3-brane) are also presented. Some new examples are discussed.

Proof of reverse isoperimetric inequality for black holes.

Paper analyzes blowup of regularized Jang solutions and constant expansion surfaces.

Dilation surfaces are generalizations of translation surfaces where the geometric structure is modelled on the complex plane up to affine maps whose linear part is real. They are the geometric framework to study suspensions of affine interval exchange maps. However, though the $SL(2,\mathbb{R})$-action is ergodic in co…

New method improves policies by combining Markov and non-Markov strategies.

We construct transformations which take asymptotically AdS hyperbolic initial data into asymptotically flat initial data, and which preserve relevant physical quantities. This is used to derive geometric inequalities in the asymptotically AdS hyperbolic setting from counterparts in the asymptotically flat realm, whenev…

Soft geometric bias improves physical dynamics predictions.

We generalize Brendle's geometric inequality considered in \cite{B} to static manifolds. The inequality bounds the integral of inverse mean curvature of an embedded mean-convex hypersurface by geometric data of the horizon. As a consequence, we obtain a reverse Penrose inequality on static asymptotically locally hyperb…

Study transverse metric expansion on null hypersurfaces, proving uniqueness for Killing horizons.

Finite-time queue peaks in stochastic networks have logarithmic scaling after geometric thresholds.

We study the effect of liquidity freezes on an economic agent optimizing her utility of consumption in a perturbed Black-Scholes-Merton model. The single risky asset follows a geometric Brownian motion but is subject to liquidity shocks, during which no trading is possible and stock dynamics are modified. The liquidity…

Firms miscount their customers who stop buying without saying goodbye.

Solves expert prediction problem for 4 experts in finite time horizon.

Study optimal stopping problems with finite-time horizon and proves continuity and strict monotonicity of the boundary.

Study optimal policy regret in partially observable Markov games with adaptive opponents.

New rigidity results for quasi-Einstein metrics with non-zero divergence-free vector fields.

We consider an individual or household endowed with an initial capital and an income, modeled as a deterministic process with a continuous drift rate. At first, we model the discounting rate as the price of a zero-coupon bond at zero under the assumption of a short rate evolving as an Ornstein-Uhlenbeck process. Then, …

In this study we model the warranty claims process and evaluate the warranty servicing costs under non-renewing and renewing free repair warranties. We assume that the repair time for rectifying the claims is non-zero and the repair cost is a function of the length of the repair time. To accommodate the ageing of the p…

Agents compose pre-trained policies for complex tasks, improving zero-shot performance.

An online reinforcement learning algorithm is anytime if it does not need to know in advance the horizon T of the experiment. A well-known technique to obtain an anytime algorithm from any non-anytime algorithm is the "Doubling Trick". In the context of adversarial or stochastic multi-armed bandits, the performance of …

We obtain a lower asymptotic bound on the decay rate of the probability of a portfolio's underperformance against a benchmark over a large time horizon. It is assumed that the prices of the securities are governed by geometric Brownian motions with the coefficients depending on an economic factor, possibly nonlinearly.…

Dynamic Black-Litterman integrates expert views with portfolio optimization over varying time horizons.

ElasTST improves time-series forecasting across varying horizons.

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…

WSqD extends learning rate schedules for large model training without fixed horizons.

Consider a discrete-time infinite horizon financial market model in which the logarithm of the stock price is a time discretization of a stochastic differential equation. Under conditions different from those given in a previous paper of ours, we prove the existence of investment opportunities producing an exponentiall…

Modeling price dynamics in response to order flow imbalance in Chinese futures markets.

We consider Blackwell approachability, a very powerful and geometric tool in game theory, used for example to design strategies of the uninformed player in repeated games with incomplete information. We extend this theory to "generalized quitting games" , a class of repeated stochastic games in which each player may ha…

In a paper \cite{P} in 1973, R. Penrose made a physical argument that the total mass of a spacetime which contains black holes with event horizons of total area $A$ should be at least $\sqrt{A/16π}$. An important special case of this physical statement translates into a very beautiful mathematical inequality in Riemann…

Study of spacelike submanifolds with umbilical lightlike normals in Lorentzian spacetimes.

New concept of Lorentzian-Euclidean black holes and metric transitions explored.

The paper establishes geometric inequalities for quasi-local masses.

ForecastGAN improves multi-horizon time series forecasting by integrating numerical and categorical features.

We construct a large class of dynamical vacuum black hole spacetimes whose exterior geometry asymptotically settles down to a fixed Schwarzschild or Kerr metric. The construction proceeds by solving a backwards scattering problem for the Einstein vacuum equations with characteristic data prescribed on the event horizon…

This study assesses the influence of the forecast horizon on the forecasting performance of several machine learning techniques. We compare the fo recast accuracy of Support Vector Regression (SVR) to Neural Network (NN) models, using a linear model as a benchmark. We focus on international tourism demand to all sevent…

This paper challenges the conventional wisdom of trend-following by showing that the medium-term horizon adds little value once short- and long-term components are included.

The paper tackles model-based RL's inaccuracy issue by dynamically adjusting planning horizons.

Proves rigidity of extremal Kerr-Newman horizons.

The paper introduces a new risk measure for financial models with jumps.

Study optimal portfolios in a non-Markovian regime-switching model with random time horizon.

We consider Kerr spacetimes with parameters a and M such that |a|<< M, Kerr-Newman spacetimes with parameters |Q|<< M, |a|<< M, and more generally, stationary axisymmetric black hole exterior spacetimes which are sufficiently close to a Schwarzschild metric with parameter M>0, with appropriate geometric assumptions on …