Study bounds for Brownian motion on manifolds with sticky boundary conditions.
problem Proving geometric bounds for Brownian motion on manifolds with sticky boundary conditions.
method Interpolation involving energy interactions between boundary and interior of the manifold.
result Explicit geometric bounds on Steklov eigenvalues, boundary trace operators, and boundary trace logarithmic Sobolev constants.
New method simulates sticky boundaries in multidimensional diffusions.
problem Simulating sticky boundaries in multidimensional diffusions.
method Approximate sticky diffusion by a Markov chain, using either finite difference or matching local moments.
result Validates both construction methods for first-order simulation schemes.
Upper bounds on constants for Brownian motion with sticky boundary.
problem Bounding constants for Brownian motion with sticky boundary.
method Interpolation approach based on energy interactions and Reilly formula.
result Upper bounds on Poincaré and Logarithmic Sobolev constants.
Estimates spectral gap for Brownian motion on sticky-reflecting domains.
problem Estimating spectral gap for Brownian motion on sticky-reflecting domains.
method Interpolation method and novel applications of Reilly formula.
result Lower bounds for spectral gap derived for general domains.
We develop continuous time Markov chain (CTMC) approximation of one-dimensional diffusions with a lower sticky boundary. Approximate solutions to the action of the Feynman-Kac operator associated with a sticky diffusion and first passage probabilities are obtained using matrix exponentials. We show how to compute matri…
In [2] the notion of stickiness for stochastic processes was introduced. It was also shown that stickiness implies absense of arbitrage in a market with proportional transaction costs. In this paper, we investigate the notion of stickiness further. In particular, we give examples of processes that are not semimartingal…
Develops a more flexible HDP-HMM for temporal data segmentation.
problem Limited expressiveness of sticky HDP-HMM due to stationary self-persistence probability.
method Introduces recurrent sticky HDP-HMM with a novel Gibbs sampling strategy.
result RS-HDP-HMM outperforms other models in segmentation tasks.
A subset of Rd is called "sticky" if it cannot be isotoped off of itself by a small ambient isotopy. Sticky wild Cantor sets are constructed in Rd for each d≥4.
Derives formula for skew stickiness ratio in asset price and volatility dynamics.
problem Capturing joint dynamics of asset price and volatility.
method Uses Itô-Wentzell and Clark-Ocone formulae to derive representation.
result Derives asymptotics of skew stickiness ratio under stochastic volatility models.
The study examines a financial model with sticky prices and finds no arbitrage when interest rate is zero.
problem Analyzing financial markets with sticky asset prices and proving no arbitrage conditions.
method Introduced a financial market model with a risky asset following a sticky geometric Brownian motion and a riskless asset with a constant interest rate. Proved no arbitrage conditions and derived pricing equations.
result No arbitrage conditions are met only when the interest rate is zero, and all replicable payoffs are derived under this condition.
New mathematical surfaces without boundaries found.
problem Existence of nonlocal free boundary minimal surfaces.
method Fractional perimeter critical points with invariant boundary.
result Existence of nonlocal free boundary minimal surfaces without boundaries.
A new model separates persistence and transition priors in HDP-HMM.
problem Limitation of sticky HDP-HMM in expressing different persistence strengths.
method Developed a disentangled sticky HDP-HMM (DS-HDP-HMM) with novel Gibbs sampling algorithms.
result DS-HDP-HMM outperforms sticky HDP-HMM and HDP-HMM on synthetic and real data.
The study introduces a new stickiness parameter for stock prices using a non-linear model.
problem Understanding how closely individual stocks follow a stock index's price movements.
method Developed a non-linear pricing model inspired by tectonic plate movements to measure stickiness.
result Defined a stickiness parameter for stock price returns using a novel model.
Model captures SPX and VIX volatility surfaces and skew-stickiness ratio.
problem Capturing volatility dynamics in financial markets.
method Two-factor Quintic Ornstein-Uhlenbeck (OU) model with polynomial volatility.
result Model accurately represents SPX and VIX volatility surfaces and SSR.
Under proportional transaction costs, a price process is said to have a consistent price system, if there is a semimartingale with an equivalent martingale measure that evolves within the bid-ask spread. We show that a continuous, multi-asset price process has a consistent price system, under arbitrarily small proporti…
Model predicts risk-adjusted returns across various financial markets.
problem Stationary models fail in predicting risk-adjusted returns due to market regime changes.
method Asset-independent regime-switching model using hidden Markov models.
result Accurately detects bull, bear, and high volatility periods for improved risk-adjusted returns.
We prove that for a so-called sticky process S there exists an equivalent probability Q and a Q-martingale S~ that is arbitrarily close to S in Lp(Q) norm. For continuous S, S~ can be chosen arbitrarily close to S in supremum norm. In the case where S is a local martingale we may choo…
As part of daily monitoring of human activities, wearable sensors and devices are becoming increasingly popular sources of data. With the advent of smartphones equipped with acceloremeter, gyroscope and camera; it is now possible to develop activity classification platforms everyone can use conveniently. In this paper,…
Study shows zero probability of cut locus for Fréchet mean on Riemannian manifolds.
problem Understanding the cut locus of Fréchet mean on Riemannian manifolds.
method Analytical proof and examples.
result Cut locus of Fréchet mean has zero probability.
SJDs unify masked, continuous, and hybrid diffusion models.
problem Unified modeling of diffusion processes.
method Continuous-time Markov processes with token embeddings and hazard rates.
result Unified model recovers masked, continuous, and hybrid diffusion as limits.
In this work, we introduce a novel class of adaptive Monte Carlo methods, called adaptive independent sticky MCMC algorithms, for efficient sampling from a generic target probability density function (pdf). The new class of algorithms employs adaptive non-parametric proposal densities which become closer and closer to …
We study in details the skew of stock option smiles, which is induced by the so-called leverage effect on the underlying -- i.e. the correlation between past returns and future square returns. This naturally explains the anomalous dependence of the skew as a function of maturity of the option. The market cap dependence…
Study bounds variance modulation function for K-spider distributions.
problem Bounding variance modulation function for K-spider distributions.
method Used folded moments and total probabilities of spider legs.
result Gave an interval for the variance modulation function.
Proposes a new financial model capturing winning and losing streaks.
problem Capturing winning and losing streaks in financial markets.
method Deep learning approach to solve high-dimensional PDE for option pricing.
result Deep learning approach accurately and efficiently solves the PDE.
New method uses hindsight to make exploration robust in stochastic environments.
problem Exploration in sparse-reward or reward-free environments, especially in stochastic settings.
method Learn representations of the future that capture unpredictable aspects, using them to predict and reward only the predictable parts of the world.
result Improves exploration in Atari games and Montezuma's Revenge, robust to stochasticity.
A new method for generating SPX and VIX risk scenarios using perturbed optimal transport.
problem Generating accurate risk estimates for SPX and VIX without full recalibration.
method A joint optimal transport calibration with perturbation methodology for sensitivities, combined with Skew Stickiness Ratio dynamics.
result The proposed method produces accurate risk estimates relative to full recalibration and is computationally faster.
New method handles large reward variations in reinforcement learning.
problem Optimal policy not achievable with existing methods for non-deterministic processes.
method Introduces conjugated distributional operator for handling real returns.
result Guaranteed theoretical convergence for a wide class of transformations.
New embeddings show answer to Baker-Laidacker question can be yes or no.
problem Answer to Baker-Laidacker question about disjoint compacta in R^N.
method Use of specific wild Cantor sets and Antoine's methods.
result Answer to Baker-Laidacker question can be twofold.
New compacta with unique embedding properties found.
problem Embedding properties of compacta in high dimensions.
method Using sticky Cantor sets and sequences of compacta.
result Construction of compacta with specific embedding properties.
The LIBOR market model is very popular for pricing interest rate derivatives, but is known to have several pitfalls. In addition, if the model is driven by a jump process, then the complexity of the drift term is growing exponentially fast (as a function of the tenor length). In this work, we consider a Lévy-driven LIB…
Model-free expression for SSR derived in terms of characteristic function.
problem Calculating the skew-stickiness-ratio (SSR) in financial markets.
method Model-free expression using characteristic function, focusing on diffusion and affine forward variance cases.
result General formula for SSR simplifies and becomes particularly tractable in affine forward variance cases, with a limit of H+3/2 for short-term limit. Study increasing profits in a flexible financial market model.
problem Characterize increasing profits in a 1D diffusion market with interest rates.
method Characterize increasing profits using an auxiliary deterministic signed measure and a canonical trading strategy.
result Existence and characterization of increasing profits in terms of ν and θ. New MCMC methods map high-dimensional problems to spheres for better mixing.
problem Mixing issues in high-dimensional distributions, especially heavy-tailed ones.
method Stereographic Markov Chain Monte Carlo (MCMC) methods that map high-dimensional problems to spheres.
result Uniformly ergodic samplers for various distributions, including heavy-tailed ones, with faster convergence in higher dimensions.
Semantically understanding complex drivers' encountering behavior, wherein two or multiple vehicles are spatially close to each other, does potentially benefit autonomous car's decision-making design. This paper presents a framework of analyzing various encountering behaviors through decomposing driving encounter data …
While absence of arbitrage in frictionless financial markets requires price processes to be semimartingales, non-semimartingales can be used to model prices in an arbitrage-free way, if proportional transaction costs are taken into account. In this paper, we show, for a class of price processes which are not necessaril…
Study on kinetic Langevin diffusions and their couplings, showing subtle TV bounds and new non-Markovian couplings.
problem Understanding and quantifying the TV distance between solutions of kinetic Langevin diffusions with different initial values.
method Established new non-Markovian couplings for kinetic Langevin diffusions, derived from optimal coalescence trajectories, and analyzed their TV bounds.
result No Markovian coupling can capture the asymptotic decay rate of the TV distance between solutions of kinetic Langevin diffusions with different initial values.
Paper proves convergence of Gini index to equilibrium in Wasserstein distance.
problem Proving convergence of Gini index to equilibrium in Wasserstein distance.
method Analyzes Gini index as Lyapunov functional and proves convergence in Wasserstein distance.
result Proves convergence of Gini index to equilibrium in Wasserstein distance.
Framework uses expert intervention to solve long-horizon reinforcement learning tasks.
problem Long horizon robot learning tasks with sparse rewards.
method Option templates and expert intervention to enable high-level task understanding.
result Framework outperforms state-of-the-art approaches by two orders of magnitude.
We consider the problem of speaker diarization, the problem of segmenting an audio recording of a meeting into temporal segments corresponding to individual speakers. The problem is rendered particularly difficult by the fact that we are not allowed to assume knowledge of the number of people participating in the meeti…
We revisit the ``Smile Dynamics'' problem, which consists in relating the implied leverage (i.e. the correlation of the at-the-money volatility with the returns of the underlying) and the skew of the option smile. The ratio between these two quantities, called ``Skew-Stickiness Ratio'' (SSR) by Bergomi (Smile Dynamics …
Decision trees are flexible models that are well suited for many statistical regression problems. In a Bayesian framework for regression trees, Markov Chain Monte Carlo (MCMC) search algorithms are required to generate samples of tree models according to their posterior probabilities. The critical component of such an …
The paper tackles multi-armed bandits with vector losses, focusing on minimizing the ℓ∞-norm of relative losses.
problem Minimizing the ℓ∞-norm of relative losses in multi-armed bandits with multiple losses. method Defines relative loss vector, derives lower bounds, and provides matching algorithms for both fixed-confidence best-arm identification and regret minimization.
result Derives problem-dependent sample complexity lower bound and matching algorithms for fixed-confidence best-arm identification.
The Local Volatility model is a well-known extension of the Black-Scholes constant volatility model whereby the volatility is dependent on both time and the underlying asset. This model can be calibrated to provide a perfect fit to a wide range of implied volatility surfaces. The model is easy to calibrate and still ve…
GDM models time series with smoother transitions and interpretable states.
problem Capturing smooth, variable-speed transitions and stochastic mixtures of states.
method Introduces a continuous relaxation of discrete states and a Gumbel noise model.
result Models real-world datasets more faithfully with smoother dynamics and interpretable states.
This work forecasts electricity prices using Bayesian regime detection and conditional neural processes.
problem Forecasting electricity prices with optimal operational outcomes.
method Bayesian regime detection with conditional neural processes, integrating multi-criteria decision support.
result R-NP model outperformed other models in comprehensive operational utility assessments.
We redefine SICR-events for better loan classification under IFRS 9.
problem Ambiguity in SICR-event definition under IFRS 9.
method Proposed alternative framework with three parameters: delinquency, stickiness, and outcome period. Varying these parameters, we generated 27 unique SICR-definitions and fitted logistic regression models.
result The proposed SICR-models outperform the PD-comparison approach as an early-warning system for credit losses.
LLMs struggle with zero-shot annotation tasks due to model-internalized priors.
problem Impact of model-internalized priors on LLM performance in zero-shot annotation tasks.
method Investigated three dimensions: familiarity, decision stickiness, and susceptibility to misaligned task definitions.
result Nearly two-thirds of zero-shot errors are resistant to correction, with a rescue rate of 34.8%. Definition-Specific Familiarity (DSF) shows a positive association with model performance.
There is by now a large consensus in modern monetary policy. This consensus has been built upon a dynamic general equilibrium model of optimal monetary policy as developed by, e.g., Goodfriend and King (1997), Clarida et al. (1999), Svensson (1999) and Woodford (2003). In this paper we extend the standard optimal monet…