We present a solution to an optimal stopping problem for a process with a wide-class of novel dynamics. The dynamics model the support/resistance line concept from financial technical analysis.
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48 results for “stopped analysis”
Early stopping for kernel boosting algorithms: A general analysis with localized complexitiesstat.ML
Early stopping of iterative algorithms is a widely-used form of regularization in statistics, commonly used in conjunction with boosting and related gradient-type algorithms. Although consistency results have been established in some settings, such estimators are less well-understood than their analogues based on penal…
Method calculates Parisian stopping times and option prices using Markov chains.
problem Computing distribution and pricing of Parisian stopping times under Markov processes.
method Continuous-time Markov chain approximation to solve for distribution and convergence analysis.
result Sharp convergence rate and efficient method for diffusion and jump models.
Stop-loss rules are often studied in the financial literature, but the stop-loss levels are seldom constructed systematically. In many papers, and indeed in practice as well, the level of the stops is too often set arbitrarily. Guided by the overarching goal in finance to maximize expected returns given available infor…
Study optimal stopping in random exploration, deriving HJB and designing a reinforcement learning algorithm.
problem Optimal stopping problem in continuous time with random exploration.
method Transformed optimal stopping to optimal control problem, derived HJB equation, designed reinforcement learning algorithm.
result Convergence rate of policy iteration and comparison to classical optimal stopping.
Trailing stop is a popular stop-loss trading strategy by which the investor will sell the asset once its price experiences a pre-specified percentage drawdown. In this paper, we study the problem of timing buy and then sell an asset subject to a trailing stop. Under a general linear diffusion framework, we study an opt…
Study optimal times to buy and sell stocks using support/resistance lines.
problem Optimal times to buy and sell stocks based on support and resistance lines.
method Mathematical model with probabilistic methods to solve optimal stopping problems.
result Best times to buy and sell stocks are determined by solving free boundary problems.
In this paper we study randomized optimal stopping problems and consider corresponding forward and backward Monte Carlo based optimisation algorithms. In particular we prove the convergence of the proposed algorithms and derive the corresponding convergence rates.
Existence of Strong Randomized Equilibria in Mean-Field Games of Optimal Stopping with Common Noisemath.OC
Existence of strong randomized equilibria in mean-field games with common noise.
problem Existence of strong solutions in mean-field games of optimal stopping.
method Connection with Bank-El Karoui's representation problem and continuity assumptions.
result Existence of strong randomized mean-field equilibrium under certain conditions.
An unconventional approach for optimal stopping under model ambiguity is introduced. Besides ambiguity itself, we take into account how ambiguity-averse an agent is. This inclusion of ambiguity attitude, via an -maxmin nonlinear expectation, renders the stopping problem time-inconsistent. We look for subgame perfect…
We use martingale and stochastic analysis techniques to study a continuous-time optimal stopping problem, in which the decision maker uses a dynamic convex risk measure to evaluate future rewards. We also find a saddle point for an equivalent zero-sum game of control and stopping, between an agent (the "stopper") who c…
Paper solves a complex stopping problem using regularization and HJB equations.
problem Time-inconsistent mean-variance optimal stopping problem
method Vanishing regularization method to derive HJB equations and prove existence of solutions
result Formally recovers variational inequalities for original problem
Early stopping is a well known approach to reduce the time complexity for performing training and model selection of large scale learning machines. On the other hand, memory/space (rather than time) complexity is the main constraint in many applications, and randomized subsampling techniques have been proposed to tackl…
The paper analyzes Variable Annuities with surrender charges, providing a pricing formula and optimal exercise boundary.
problem Analyzing Variable Annuities with surrender charges and early termination rights.
method Formulated as an optimal stopping problem with a discontinuous payoff, non-monotonic optimal stopping boundaries are proven continuous and regular.
result A rigorous pricing formula and optimal exercise boundary for surrender options are derived.
New algorithms use Gaussian processes to optimize stopping times in financial markets.
problem Optimizing stopping times in financial time series with specific applications.
method Gaussian and Deep Gaussian Process models to analytically evaluate optimal stopping value functions and policies.
result Proposed algorithms outperform benchmarks on various financial time series datasets.
Study optimal stopping for diffusion processes using data-driven methods.
problem Optimal stopping for diffusion processes under unknown conditions.
method Data-driven approach, deriving upper and lower bounds on simple and cumulative regret.
result Verified minimax optimality and improved convergence rates.
Early stopping improves neural networks' performance on binary classification tasks.
problem Improving shallow ReLU networks' performance on binary classification tasks.
method Gradient descent with early stopping on binary classification data.
result Gradient descent with early stopping achieves population risk arbitrarily close to optimal.
Stopping Criterion Design for Recursive Bayesian Classification: Analysis and Decision Geometrycs.LG
The paper analyzes and proposes a new stopping criterion for recursive Bayesian classification.
problem Limitations of conventional stopping criteria in recursive Bayesian classification.
method Geometric interpretation of state posterior progression and analysis of conventional criteria.
result Proposes a new stopping criterion to overcome limitations of conventional methods.
Sharp analysis of power iteration for tensor PCA, improving convergence and stopping criteria.
problem Analyzing the power iteration algorithm for tensor PCA to improve convergence and stopping criteria.
method Sharp bounds on the number of iterations, revealing a smaller algorithmic threshold, proposing a stopping criterion.
result Sharp bounds on the number of iterations required for power method to converge, revealing a smaller algorithmic threshold than previously conjectured.
Risk-Neutral Pricing Model of Uniswap Liquidity Providing Position: A Stopping Time Approachq-fin.PR
Paper introduces a new pricing model for Uniswap V3 positions.
problem Valuation of Uniswap V3 liquidity positions.
method Stochastic processes and Martingale Stopping Theorem.
result Model provides significant insights into risk exposure and hedging strategies.
Paper proposes a method for early stopping in regression using reproducing kernels.
problem Early stopping for iterative learning algorithms in nonparametric regression.
method Data-driven rule based on minimum discrepancy principle, validated by fixed-point analysis of localized Rademacher complexities.
result The proposed rule is minimax-optimal and performs comparably to cross-validation.
Study on deep neural networks using concentration inequalities and optimal stopping.
problem Understanding the performance and structure of stochastic deep neural networks.
method Introduced concentration inequalities for SDNN outputs and an EC classifier. Determined the optimal number of layers via an optimal stopping procedure.
result Optimal number of layers for SDNNs determined via an optimal stopping procedure.
Analysis of cross-validation for early-stopped gradient descent in high-dimensional regression.
problem Inconsistency of GCV for early-stopped GD in high-dimensional least squares regression.
method Theoretical analysis of GCV and LOOCV applied to early-stopped GD in high-dimensional least squares regression.
result LOOCV converges uniformly to the prediction risk of early-stopped GD, while GCV is generically inconsistent.
Nearly Minimax-Optimal Rates for Noisy Sparse Phase Retrieval via Early-Stopped Mirror Descenteess.SP
Paper studies early-stopped mirror descent for noisy sparse phase retrieval.
problem Recovering a sparse signal from noisy quadratic measurements.
method Early-stopped mirror descent with hyperbolic entropy mirror map.
result Achieves nearly minimax-optimal rate of convergence for -sparse signals.
We propose a strategy for automated trading, outline theoretical justification of the profitability of this strategy and overview the hypothetical results in application to currency pairs trading. The proposed methodology relies on the assumption that processes reflecting the dynamics of currency exchange rates are in …
Neural networks solve variational inequalities for optimal stopping problems.
problem Solving variational inequalities for optimal stopping problems in finance.
method Proposed neural network approach using loss functions directly incorporating variational inequality on whole domain.
result Existence and convergence of neural networks whose losses converge to zero.
RankNet forecasts car racing positions with improved accuracy and stability.
problem Forecasting rank positions in car racing, especially considering pit stops.
method Cause-effect decomposition in RankNet, incorporating probabilistic forecasting.
result RankNet outperforms baselines significantly, improving MAE by over 10%.
We give a complete characterization of the complexity of best-arm identification in one-parameter bandit problems. We prove a new, tight lower bound on the sample complexity. We propose the `Track-and-Stop' strategy, which we prove to be asymptotically optimal. It consists in a new sampling rule (which tracks the optim…
This paper addresses the question of how an arbitrage-free semimartingale model is affected when stopped at a random horizon. We focus on No-Unbounded-Profit-with-Bounded-Risk (called NUPBR hereafter) concept, which is also known in the literature as the first kind of non-arbitrage. For this non-arbitrage notion, we ob…
This study analyzes AdaGrad's stability and convergence in non-convex optimization.
problem Lack of theoretical analysis for AdaGrad in non-convex optimization.
method Novel stopping time-based techniques from probability theory.
result Established stability and derived convergence rates for AdaGrad.
Stop-loss and Leverage in optimal Statistical Arbitrage with an application to Energy marketq-fin.PM
In this paper we develop a statistical arbitrage trading strategy with two key elements in hi-frequency trading: stop-loss and leverage. We consider, as in Bertram (2009), a mean-reverting process for the security price with proportional transaction costs; we show how to introduce stop-loss and leverage in an optimal t…
Fast and Regret Optimal Best Arm Identification: Fundamental Limits and Low-Complexity Algorithmscs.LG
This paper solves the best arm identification problem with both quick commitment and reward maximization.
problem Simultaneously identifying the best arm and minimizing regret in a stochastic Multi-Armed Bandit problem.
method Introduces Regret Optimal Best Arm Identification (ROBAI) and presents algorithms EOCP and its variants.
result Achieves asymptotic optimal regret and quick commitment to the optimal arm in both pre-determined and adaptive stopping times.
In this paper we study the stochastic area swept by a regular time-homogeneous diffusion till a stopping time. This unifies some recent literature in this area. Through stochastic time change we establish a link between the stochastic area and the stopping time of another associated time-homogeneous diffusion. Then we …
We introduce new variants of classical regression-based algorithms for optimal stopping problems based on computation of regression coefficients by Monte Carlo approximation of the corresponding inner products instead of the least-squares error functional. Coupled with new proposals for simulation of the underlyi…
We develop a probabilistic framework for sequential random projection.
problem Challenges of sequential decision-making under uncertainty.
method Novel construction of a stopped process and method of mixtures.
result Achieved a non-asymptotic probability bound for random projection.
For an infinite-horizon continuous-time optimal stopping problem under non-exponential discounting, we look for an optimal equilibrium, which generates larger values than any other equilibrium does on the entire state space. When the discount function is log sub-additive and the state process is one-dimensional, an opt…
Solves optimal stopping problem with Poisson constraints using jumps.
problem Optimal stopping with Poisson constraints and jumps.
method Penalized backward stochastic differential equation (PBSDE) with jumps, decomposition method based on Jacod-Pham, comparison theorem of BSDEs with jumps.
result Solves American option pricing in nonlinear markets with Poisson constraints.
Neural Optimal Stopping Boundaryq-fin.PR
Neural networks optimize stopping boundaries in financial instruments.
problem Optimizing stopping boundaries in financial instruments.
method Deep neural networks and empirical risk minimization for parameterizing stopping boundaries.
result Proved existence of stopping boundary under natural assumptions.
Within the natural language processing (NLP) community, active learning has been widely investigated and applied in order to alleviate the annotation bottleneck faced by developers of new NLP systems and technologies. This paper presents the first theoretical analysis of stopping active learning based on stabilizing pr…
Stochastic Gradient Descent in Hilbert Scales: Smoothness, Preconditioning and Earlier Stoppingstat.ML
Stochastic Gradient Descent improved for various Hilbert scales and misspecified models.
problem Understanding and optimizing SGD in Hilbert scales for machine learning.
method Extending SGD analysis to Hilbert scales, including Sobolev and Diffusion spaces, and showing the effects of smoothness and preconditioning.
result Violation of smoothness assumption affects learning rate; preconditioning in Hilbert scales reduces the number of iterations for misspecified models.
New method stops experiments early for harm in diverse groups.
problem Early stopping of experiments for harmful treatment effects in diverse populations.
method Causal machine learning approach (CLASH) for early stopping.
result CLASH effectively stops experiments early for harmful treatment effects in diverse groups.
We introduce techniques for exploring the functionality of a neural network and extracting simple, human-readable approximations to its performance. By performing gradient ascent on the input space of the network, we are able to produce large populations of artificial events which strongly excite a given classifier. By…
Kalman-based Stochastic Gradient Method with Stop Condition and Insensitivity to Conditioningmath.OC
Modern proximal and stochastic gradient descent (SGD) methods are believed to efficiently minimize large composite objective functions, but such methods have two algorithmic challenges: (1) a lack of fast or justified stop conditions, and (2) sensitivity to the objective function's conditioning. In response to the firs…
A survey of existing methods for stopping active learning (AL) reveals the needs for methods that are: more widely applicable; more aggressive in saving annotations; and more stable across changing datasets. A new method for stopping AL based on stabilizing predictions is presented that addresses these needs. Furthermo…
In this work we consider optimal stopping problems with conditional convex risk measures called optimised certainty equivalents. Without assuming any kind of time-consistency for the underlying family of risk measures, we derive a novel representation for the solution of the optimal stopping problem. In particular, we …
Optimal timing for converting savings into annuities considering mortality risk.
problem Determining the best time to annuitize retirement savings under stochastic mortality.
method Formulated as a three-dimensional optimal stopping problem, reduced to nested one-dimensional problems, solved using PDMP structure.
result Rich structure for the optimal annuitization rule, covering various parameter specifications.
Unified approach to stochastic control, filtering, and stopping using rough paths.
problem Addressing gaps in classical problems of stochastic control, filtering, and stopping.
method Combining rough path theory with controlled rough paths to provide a pathwise deterministic framework.
result Established rigorous connection between candidate solutions and Hamilton-Jacobi-Bellman equation.
Top2Vec finds topic vectors from documents and words without needing stop words or custom settings.
problem Topic modeling weaknesses, including needing known topics, stop words, and custom settings.
method Joint document and word semantic embedding to find topic vectors automatically.
result Top2Vec finds more informative and representative topics than probabilistic models.