New principle reduces load imbalance in LLM serving systems, saving up to 52% energy.
problem Wasted computational power due to load imbalance in LLM serving systems.
method Developed a universal load-balancing principle for barrier-synchronized systems with non-migratable state.
result Proves worst-case theoretical guarantees for imbalance reduction and energy savings.
L3Ms fine-tune LLMs with constraints for tailored applications.
problem Inadequate alignment of LLMs for diverse applications.
method Formulate SFT and alignment as constrained optimization, using logarithmic barriers.
result Versatile and effective in achieving tailored alignments for various applications.
Study on generating and identifying languages privately, showing privacy imposes costs and creates barriers.
problem Generating and identifying languages privately in the limit model.
method Introduced a continual release model under differential privacy constraints, proving both positive and negative results.
result Privacy imposes quantitative and qualitative costs, and creates fundamental barriers for identification.
Machine learning aids in bridging international news gaps.
problem Limited global understanding due to segmented news and language barriers.
method Combining machine learning, journalism studies, and statistics.
result Improved global perspective on international issues.
Reducing barriers to entry in large-scale ML markets, study shows multi-objective learning can lower data requirements.
problem Barriers to entry in emerging markets for large-scale machine learning models.
method Defined a multi-objective high-dimensional regression framework to study reputational damage and data requirements.
result The number of data points needed for a new company to enter the market can be significantly smaller than the incumbent company's dataset size.
LeanDojo removes barriers to theorem proving with open-source tools and data.
problem Difficulty in reproducing and building on existing theorem proving methods.
method Introduces LeanDojo, an open-source Lean playground with toolkits, data, models, and benchmarks.
result ReProver, an LLM-based prover augmented with retrieval, outperforms non-retrieval baselines and GPT-4.
SpanishTinyRoBERTa distills large Spanish models into efficient question-answering models.
problem Efficient Spanish question-answering models for resource-constrained environments.
method Knowledge distillation from large Spanish language models onto a smaller model.
result SpanishTinyRoBERTa achieves comparable performance to large models with faster inference.
The paper calculates prices for multi-step barrier options under the Black-Scholes model.
problem Calculating prices for multi-step barrier options with varying barriers and time steps.
method Derives a general, explicit expression for option prices using the Black-Scholes model and a multi-step reflection principle.
result Derives a multi-step reflection principle that generalizes the reflection principle of Brownian motion.
We demonstrate effectiveness of the first-order algorithm from [Milstein, Tretyakov. Theory Prob. Appl. 47 (2002), 53-68] in application to barrier option pricing. The algorithm uses the weak Euler approximation far from barriers and a special construction motivated by linear interpolation of the price near barriers. I…
A new method uses deep learning to price barrier options.
problem Pricing barrier options with boundary conditions.
method Forward deep BSDEs with added nodes for barrier conditions.
result Can handle any barrier condition and boundary conditions.
Pricing bonus certificates and barrier products uses efficient interpolation and stochastic modeling.
problem Pricing bonus certificates and barrier products with American conditions.
method Efficient interpolation for European conditions, stochastic modeling for American conditions.
result Pricing can be done without stochastic modeling within a certain accuracy range.
In2Core selects a coreset for efficient LLM fine-tuning with reduced data.
problem Costly fine-tuning of large language models due to extensive parameters and data requirements.
method Analyzes model gradients to estimate training sample influence, optimizing for efficiency.
result Achieves similar performance with 50% of training data using In2Core.
We determine the price of digital double barrier options with an arbitrary number of barrier periods in the Black-Scholes model. This means that the barriers are active during some time intervals, but are switched off in between. As an application, we calculate the value of a structure floor for structured notes whose …
A time-dependent double-barrier option is a derivative security that delivers the terminal value φ(ST) at expiry T if neither of the continuous time-dependent barriers $b_\pm:[0,T]\to \RR_+$ have been hit during the time interval [0,T]. Using a probabilistic approach we obtain a decomposition of the barrier opti…
Efficient semi-analytic methods for pricing double barrier options with time-dependent parameters.
problem Pricing and calibration of double barrier options with time-dependent parameters.
method Two approaches: General Integral transform method and Heat Potential method.
result Semi-analytic techniques are more efficient for pricing double barrier options than traditional numerical methods.
We provided an analytical representation of the price of a barrier option with one type of special moving barrier. We consider the case that risk free rate, dividend rate and stock volatility are time dependent. We get a pricing formula and put call parity for barrier option when the moving barrier has a special relati…
Hamiltonian method applied to floating barrier options pricing.
problem Pricing of floating barrier options.
method Hamiltonian approach in quantum mechanics applied to barrier options.
result Analytical expressions for pricing kernel and option price derived.
New method improves barrier option pricing for high volatility assets.
problem Efficient pricing of barrier options on high volatility assets.
method Subset Simulation for barrier option pricing.
result The method outperforms standard Monte Carlo and multilevel Monte Carlo approaches.
Deep learning solves barrier options with stochastic volatility.
problem Solving barrier options with stochastic volatility.
method Unsupervised deep learning neural networks trained to satisfy PDE and boundary conditions.
result Neural networks accurately price barrier options in a single framework.
New method tackles bilevel optimization with polyhedral constraints.
problem Challenges in bilevel optimization with active-set changes and expensive Hessian inversions.
method Logarithmic barrier smoothing and proxy-gradient algorithm for differentiable approximation.
result Stationarity rates of O(K−2/3) in deterministic setting and O(K−2/5) under stochastic noise. Unified pricing method for FX options with barriers.
problem Calculating the value and sensitivities of FX options with barriers.
method Unified Vanna-Volga pricing technique for single and double barrier FX options.
result Derivation of closed formulas for Delta, Vega, Vanna, and Volga.
Root's barrier is continuous and finite under certain conditions.
problem Continuity of the root barrier function.
method Analyzing Skorokhod embedding problem and properties of target measures.
result The barrier function is continuous and finite under specified conditions.
New method calculates barrier option Greeks using Wiener path integrals.
problem Computing first-order Greeks for barrier options efficiently.
method Developed chain rules for Wiener path integrals.
result Effectiveness demonstrated through numerical examples.
Path integral method calculates barrier option prices.
problem Barrier option pricing in finance.
method Path integral method applied to trapezoid and square potential barriers.
result Analytical expressions for option pricing derived.
This paper deals with a high-order accurate implicit finite-difference approach to the pricing of barrier options. In this way various types of barrier options are priced, including barrier options paying rebates, and options on dividend-paying-stocks. Moreover, the barriers may be monitored either continuously or disc…
Framework for pricing and replicating barrier-style claims on asset price and volatility.
problem Pricing and replicating barrier-style claims on price and volatility.
method Assumes no arbitrage, frictionless markets, zero interest rates. Models risky asset as strictly positive continuous semimartingale with independent volatility process.
result Shows how to price and replicate barrier-style claims using the underlying asset, zero-coupon bonds, and European calls/puts.
ChemCrow enhances LLMs for chemistry tasks, automating complex chemical processes.
problem Limited access to computational chemistry tools for large-language models.
method Integrating 18 expert-designed chemistry tools into an LLM (ChemCrow).
result ChemCrow autonomously plans and executes chemical syntheses and discoveries.
New Monte Carlo method for calculating sensitivities of barrier options.
problem Calculating sensitivities for discontinuous payoff functions in barrier options.
method Combining one-step survival idea with stable differentiation approach.
result Calculated sensitivities for different types of barrier options.
Study examines optimal hedging of barrier options in leptokurtic equity returns.
problem Optimal hedging of barrier options in a leptokurtic equity market.
method Discretely sampled exponential Lévy model calibrated to equity returns.
result Hedging errors significantly impact barrier option prices.
Analyzes pricing formulas for barrier options with discrete dividends.
problem Complexity introduced by discrete dividends in pricing formulas.
method Compares Buryak and Guo's analytic approach for European options with Dai and Chiu's barrier option formulas.
result Analytic approach effective for European puts and calls, but performance varies for barrier options.
Research provides explicit NPV expressions for double barrier strategies.
problem Calculating expected NPVs of double barrier strategies for regular diffusions.
method Explicit expression using bivariate q-scale function with perturbation technique.
result Explicit expressions for expected NPVs are derived for certain cases.
New symplectic barriers found in ball embeddings.
problem Existence of symplectic embeddings with intersections.
method Proving obligatory intersections with symplectic planes.
result Existence of symplectic barriers in ball embeddings.
The paper studies how convex surfaces shrink under mean curvature flow with a free boundary.
problem Mean curvature flow of convex surfaces with a free boundary on convex barriers.
method Introduced a new perturbation argument to establish convexity and pinching estimates.
result The flow contracts a sufficiently convex surface to a point in finite time, asymptotic to a half-sphere.
Paper applies subdiffusive dynamics to American and barrier options pricing.
problem Valuation of American and barrier options in subdiffusive financial models.
method Proposes weighted finite difference and Longstaff-Schwartz methods for valuation.
result Numerical valuation of American and barrier options demonstrated.
We use Lie symmetry methods to price certain types of barrier options. Usually Lie symmetry methods cannot be used to solve the Black-Scholes equation for options because the function defining the maturity condition for an option is not smooth. However, for barrier options, this restriction can be accommodated and a sy…
In this paper we analyse financial implications of exchangeability and similar properties of finite dimensional random vectors. We show how these properties are reflected in prices of some basket options in view of the well-known put-call symmetry property and the duality principle in option pricing. A particular atten…
We say that a topologically embedded 3-sphere in a smoothing of Euclidean 4-space is a barrier provided, roughly, no diffeomorphism of the 4-manifold moves the 3-sphere off itself. In this paper we construct infinitely many one parameter families of distinct smoothings of 4-space with barrier 3-spheres. \par The existe…
BDH model learns like the brain, rivaling Transformer performance.
problem Leveraging brain-like properties for machine learning.
method Scale-free biologically inspired network of neuron particles.
result BDH model achieves Transformer-like performance with interpretability.
We derive a forward equation for arbitrage-free barrier option prices, in terms of Markovian projections of the stochastic volatility process, in continuous semi-martingale models. This provides a Dupire-type formula for the coefficient derived by Brunick and Shreve for their mimicking diffusion and can be interpreted …
New formulas for barrier options in stochastic volatility models with nonzero correlation.
problem Calculating barrier options prices in models with nonzero correlation.
method Derivation of two novel closed-form formulas: Hull and White type and Alòs-like decomposition.
result Closed-form formulas for barrier options in stochastic volatility models with nonzero correlation.
In-Place TTT enhances LLMs with dynamic parameter updates at inference time.
problem Static training limits LLMs from adapting to new information.
method In-Place TTT updates a subset of model parameters (fast weights) at inference time.
result In-Place TTT enables 4B-parameter models to outperform on tasks with up to 128k contexts.
This note re-addresses the Paris barrier options proposed by Yor and collaborators and their valuation using the Laplace transform approach. The notion of Paris barrier options, based on excursion theory and using the Brownian meander, is extended such that their valuation is now possible at any point during their life…
Develops a new flow with free boundary in barrier surfaces.
problem Free-boundary problems in barrier surfaces.
method Develops Brakke flow with free boundary, proves compactness, Gaussian monotonicity, and existence.
result Proves existence of free-boundary Brakke flows.
Bayesian method synthesizes barrier certificates for unknown systems with latent states.
problem Certifying safety in systems with unknown dynamics and latent states.
method Bayesian inference with Metropolis-Hastings sampler and sum-of-squares program.
result Probabilistic validity of barrier certificates for unknown systems.
We approximate prices of various financial claims using a combination of expansions.
problem Approximating prices of financial claims in a complex volatility setting.
method Combining Taylor series expansions of diffusion coefficients with an expansion in correlation parameter.
result Rigorous accuracy results for European-style claims, and numerical examples for barrier-style claims.
Analytical model prices options with moving barriers under non-Gaussian distributions.
problem Pricing options with moving barriers under non-Gaussian distributions.
method Path-integral formalism adapted from galaxy formation models, incorporating higher-order cumulants.
result Analytical pricing model for vanilla and barrier options without volatility smile.
Study short-term behavior of up-and-in barrier options using Malliavin calculus.
problem Analyzing the decay rate of up-and-in barrier option prices as maturity decreases.
method Use Malliavin calculus to analyze the law of the supremum of the log-price process.
result Derive upper bound on asymptotic decay rate of up-and-in barrier option prices.
This paper presents a new asymptotic expansion method for pricing continuously monitoring barrier options. In particular, we develops a semi-group expansion scheme for the Cauchy-Dirichlet problem in the second-order parabolic partial differential equations (PDEs) arising in barrier option pricing. As an application, w…