Explains Uhlenbeck's work on maps and fields.
problem None explicitly stated in the abstract.
method Expository discussion of Uhlenbeck's work on harmonic maps and Yang-Mills fields.
result Discussion of Uhlenbeck's contributions to mathematical fields.
New proofs of Donaldson-Uhlenbeck-Yau theorem using geodesic rays.
problem Donaldson-Uhlenbeck-Yau theorem implications
method Geodesic rays of Hermitian metrics
result New proofs of the theorem
Characterizes Lévy-driven Ornstein-Uhlenbeck processes linked to tempered stable distributions.
problem Understanding Lévy-driven Ornstein-Uhlenbeck processes and their properties.
method Characterizes the Lévy triplet and deduces transition laws for finite variation Ornstein-Uhlenbeck processes associated with tempered stable distributions.
result Provides algorithms for generating skeleton of Ornstein-Uhlenbeck processes related to exponentially-modulated tempered stable laws.
Sacks-Uhlenbeck's result on metric spaces expanded.
problem Existence of non-trivial harmonic 2-spheres in metric spaces.
method Developed a metric approach to generalize Sacks-Uhlenbeck's result.
result Generalized Sacks-Uhlenbeck's result to a broader class of compact metric spaces.
This research announcement gives a brief report of the main results in our paper "PU(2) monopoles, I: Regularity, Uhlenbeck compactness, and transversality" (Journal of Differential Geometry, to appear). We describe the existence of perturbations for the PU(2) monopole equations, yielding both useful transversality pro…
Pairs trading strategy improved using Ornstein-Uhlenbeck process.
problem Improving pairs trading strategy effectiveness.
method Used Ornstein-Uhlenbeck process to model stock price spreads.
result OU model captures signals and trends effectively but underperforms compared to naive model.
Entropy-minimal measure calculated for a stochastic volatility model.
problem Calculating the entropy-minimal equivalent martingale measure in a stochastic volatility model.
method Revised related theory, calculated entropy-minimal measure.
result Entropy-minimal measure for the exponential Ornstein-Uhlenbeck model.
Extends optimal regularity and Uhlenbeck compactness to non-Riemannian manifolds.
problem Establishing optimal regularity and compactness for connections on vector bundles over non-Riemannian manifolds.
method Proofs based on RT-equations for connections with Lp curvature, extending to non-compact gauge groups. result Removes singularities at GR shock waves, ensuring existence of geodesics and coordinates.
A new fast method simulates stochastic volatility models.
problem Simulating stochastic volatility models efficiently.
method Karhunen-Loève expansions to express stochastic volatility as sine series, followed by analytical derivation of integrals.
result Simulation is several hundred times faster than existing methods.
Develops European power option pricing under correlated interest rate and asset processes.
problem Pricing European power options under correlated interest rate and asset processes.
method Martingale method and Girsannov transform.
result Derives European power option pricing formulae under two market assumptions.
We will give a weak energy identity for Sacks-Uhlenbeck approximation of harmonic maps and calculate the length of the necks.
This paper proves a general Uhlenbeck compactness theorem for sequences of solutions of Yang-Mills flow on Riemannian manifolds of dimension n≥4, including rectifiability of the singular set at finite or infinite time.
We prove sharp bounds for the growth rate of eigenfunctions of the Ornstein-Uhlenbeck operator and its natural generalizations. The bounds are sharp even up to lower order terms and have important applications to geometric flows.
Paper models non-maturing deposits using a Lévy-driven Ornstein-Uhlenbeck process.
problem Managing non-maturing deposits as a major funding source for banks.
method Develops a multivariate Lévy-driven Ornstein-Uhlenbeck process with three sources of randomness.
result Models rare but severe events in deposit volumes with positive probability.
Study optimal strategy for maximizing exponential utility in financial market with linear price impact.
problem Maximizing exponential utility in financial market with linear price impact.
method Purely probabilistic approach using duality.
result Computed optimal portfolio strategy and value for Ornstein-Uhlenbeck process.
The paper proves a Donaldson-Uhlenbeck-Yau theorem for normal varieties and semistable bundles.
problem Proving a Donaldson-Uhlenbeck-Yau theorem for normal varieties and semistable bundles.
method Analyzing degenerating families of projective normal varieties and studying the limiting behavior of semistable bundles.
result Improves several previously known algebro-geometric results on normalized tautological classes and proves a new version of the singular Donaldson-Uhlenbeck-Yau theorem.
Model approximates market prices and returns without prior market dynamics.
problem Simultaneously approximate market prices and log returns.
method GDN model of Kratsios and Papon (2022) for generalized Ornstein-Uhlenbeck process.
result Universal approximation guarantees for conditional distributions and contingent claims.
We consider the Black--Scholes model of financial market modified to capture the stochastic nature of volatility observed at real financial markets. For volatility driven by the Ornstein--Uhlenbeck process, we establish the existence of equivalent martingale measure in the market model. The option is priced with respec…
When stock prices are observed at high frequencies, more information can be utilized in estimation of parameters of the price process. However, high-frequency data are contaminated by the market microstructure noise which causes significant bias in parameter estimation when not taken into account. We propose an estimat…
Study on gamma-related OU processes with simulation methods.
problem Distributional properties and simulation of gamma-related OU processes.
method Investigation of gamma and bilateral gamma laws, derivation of closed-form densities and characteristic functions, and development of efficient simulation algorithms.
result Efficient algorithms for generating gamma-related OU processes with significantly faster performance than existing methods.
Method verifies if observed data fits Lévy-Driven Ornstein-Uhlenbeck process.
problem Verifying if observed data fits Lévy-Driven Ornstein-Uhlenbeck process.
method Estimating parameters and approximating the driving process to test CAR(1) Lévy-driven hypothesis.
result Demonstrates method's effectiveness through simulations and real data examples.
Study optimizes dividend payout strategies under fluctuating interest rates.
problem Maximizing dividends under stochastic interest rates with negative values.
method Analytical HJB approach and backward SDEs for analysis.
result Explicit optimal strategies found for both time-dependent and strategy-independent stopping times.
In 1982, Uhlenbeck \cite {U2} established the well-known gauge fixing theorem, which has played a fundamental role for Yang-Mills theory. In this paper, we apply the idea of Uhlenbeck to establish a parabolic type of gauge fixing theorems for the Yang-Mills flow and prove existence of a weak solution of the Yang-Mills …
Karen Uhlenbeck's compactness theorem for sequences of connections with L2 bounds on curvature applies only to connections on principal bundles with compact structure group. This article states and proves an extension of Uhlenbecks theorem that describes sequences of connections on principal PSL(2;C) bundles over compa…
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 …
Modeling horse race betting odds with Ornstein-Uhlenbeck process.
problem Analyzing how herding and informed bettors affect odds movements.
method Deriving an Ornstein-Uhlenbeck process from vote shares and odds movements data.
result Identified microscopic and macroscopic patterns in odds convergence.
Study prices energy derivatives using specific stochastic processes.
problem Pricing energy derivatives in markets driven by specific stochastic processes.
method Calculated characteristic functions, derived non-arbitrage conditions, and developed efficient algorithms for simulation.
result Developed methods for pricing various energy contracts.
In this paper, we study an α-flow for the Sack-Uhlenbeck functional on Riemannian surfaces and prove that the limiting map by the α-flows is a weak solution to the harmonic map flow. By an application of the α-flow, we present a simple proof of an energy identity of a minimizing sequence in each homotopy class.
Uhlenbeck's compactness theorem can be used to analyze sequences of connections with anti-self dual curvature on principal SU(2) bundles over oriented 4-dimensional manifolds. The theorems in this paper give an extension of Uhlenbeck's theorem for sequences of solutions of certain SL(2,C) analogs of the anti-self dual …
We prove that any flat family (Fu)u∈U of rank 2 torsion-free sheaves on a Gauduchon surface defines a continuous map on the semi-stable locus Uss:={u∈U ∣ Fu is slope semi-stable} with values in the Donaldson-Uhlenbeck compactification of the corresponding in…
New conservation laws found for polyharmonic maps in critical dimension.
problem Existence of conservation laws for polyharmonic maps in critical dimension.
method Small perturbation of Uhlenbeck's gauge fixing matrix.
result Existence of conservation laws for elliptic systems of even order in critical dimension.
The aim of this paper is to construct the parabolic version of the Donaldson--Uhlenbeck compactification for the moduli space of parabolic stable bundles on an algenraic surface with parabolic structures along a divisor with normal crossing singularities. We prove the non--emptiness of the moduli space of parabolic sta…
A new volatility model calibrates SPX & VIX smiles with 6 parameters.
problem Joint calibration of SPX and VIX smiles with a simple model.
method Quintic Ornstein-Uhlenbeck volatility model with polynomial volatility process.
result Remarkable joint fits of SPX-VIX smiles with only 6 parameters.
Extends optimal regularity and compactness to vector bundles over non-Riemannian manifolds.
problem Optimal regularity and compactness for connections on vector bundles.
method Derive RT-equations, establish existence theory, handle curvature up to L1. result Optimal regularity and compactness extended to vector bundles over non-Riemannian manifolds.
We study the pricing problem for a European call option when the volatility of the underlying asset is random and follows the exponential Ornstein-Uhlenbeck model. The random diffusion model proposed is a two-dimensional market process that takes a log-Brownian motion to describe price dynamics and an Ornstein-Uhlenbec…
Stability of Morse index for Yang-Mills connections in 4D.
problem Stability of critical points in Yang-Mills energy relaxation.
method Establishing lower semi-continuity of Morse index and upper continuity of Morse index plus nullity.
result Yang-Mills fields are more stable than harmonic maps in 4D.
The paper explores how score-driven models can approximate rough volatility.
problem Modeling rough volatility with long memory structures.
method Extending score-driven models to include infinite-lag structures and heavy-tailed decay.
result Score-driven models converge to fractional Ornstein-Uhlenbeck processes under appropriate scaling.
Study optimal futures trading strategies for assets with multiscale central tendency price model.
problem Optimal dynamic trading of futures with multiscale central tendency price model.
method Derive no-arbitrage futures prices, solve HJB equations for optimal strategies.
result Optimal trading strategies depend on asset parameters and futures risk premia.
Study on Yang-Mills equation near instanton-anti-instanton configurations with energy constraints.
problem Understanding Yang-Mills connections near instanton-anti-instanton configurations.
method Analyzing the Uhlenbeck limit and bubble configurations, determining obstructions and proving solutions.
result Instantons are the only solutions with energy less than $4π^2 \left( |κ| + 2
ight) + \varepsilon_κ$.
Deep learning outperforms traditional methods in estimating OU process parameters.
problem Parameter estimation of the Ornstein-Uhlenbeck process is challenging.
method Used a multi-layer perceptron to estimate OU process parameters compared to traditional methods like Kalman filter and maximum likelihood estimation.
result Deep learning method outperforms traditional methods in parameter estimation of the OU process.
Pricing of European basket call option with n-assets and a bond is discussed in this paper, where all prices of n-assets and the bond are driven by Exponential Ornstein-Uhlenbeck processes. The close-form of European basket option pricing formula is derived. Utilizing with 1-order differential approximate numerical sol…
We consider a spread financial market defined by the multidimensional Ornstein--Uhlenbeck (OU) process. We study the optimal consumption/investment problem for logarithmic utility functions in the base of stochastic dynamical programming method. We show a special Verification Theorem for this case. We find the solution…
Study simulates Variance Gamma processes for energy derivatives pricing.
problem Simulating Variance Gamma processes for accurate energy derivative pricing.
method Three-step procedure to relate self-decomposability to increments, derived from Qu et al. (2019). Exact simulation of skeleton of Variance Gamma and symmetric Variance Gamma driven Ornstein-Uhlenbeck processes.
result Exact simulation of Variance Gamma and related processes without numerical inversion.
Two new models for volatility in Markov-switching environments capture financial time-series properties.
problem Modeling volatility in environments with regime switches and exogenous jumps.
method Generalizations of COGARCH and Barndorff-Nielsen-Shephard models using Markov-modulated generalized Ornstein-Uhlenbeck processes.
result Models inherit properties of original models and capture stylized facts of financial time-series.
Approximates derivative pricing under fractional stochastic volatility.
problem Derivative pricing under fractional stochastic volatility model.
method Approximate expression derived from deterministic functions and fractional Ornstein-Uhlenbeck process.
result Numerical simulations show the feasibility and effect of long-range dependencies on derivative prices.
Given the observation of a high-dimensional Ornstein-Uhlenbeck (OU) process in continuous time, we proceed to the inference of the drift parameter under a row-sparsity assumption. Towards that aim, we consider the negative log-likelihood of the process, penalized by an ℓ1-penalization (Lasso and Adaptive Lasso). …
The study investigates noise effects on parameter estimation for Ornstein-Uhlenbeck processes.
problem Impact of noise on parameter fitting for Ornstein-Uhlenbeck processes.
method Proposed algorithms to distinguish between thermal and multiplicative noise.
result Effective methods to estimate parameters even when multiplicative noise dominates.
We prove an analogue of the Donaldson-Uhlenbeck-Yau theorem for asymptotically cylindrical Kähler manifolds: If E is a reflexive sheaf over an ACyl Kähler manifold, which is asymptotic to a μ-stable holomorphic vector bundle, then it admits an asymptotically translation-invariant protectively Hermitian Ya…