We prove uniqueness of instantaneously complete Ricci flows on surfaces. We do not require any bounds of any form on the curvature or its growth at infinity, nor on the metric or its growth (other than that implied by instantaneous completeness). Coupled with earlier work, particularly [23, 11], this completes the well…
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48 results for “instantaneously complete”
Global existence of Yamabe flows on hyperbolic space proved without curvature bounds.
problem Global existence of Yamabe flows on hyperbolic space without completeness or curvature bounds.
method Instantaneously complete initial metrics, no curvature bounds required.
result Global existence of Yamabe flows on hyperbolic space of arbitrary dimension .
Study on Yamabe flow on manifolds with singularities, proving removability.
problem Yamabe flow on manifolds with submanifold singularities.
method Analyzing the Yamabe flow on Riemannian manifolds of dimension minus a closed submanifold of dimension .
result Removability of singularities preserved along the Yamabe flow in certain cases.
The Ricci flow preserves product structures with instantaneous curvature bounds.
problem Preserving product structures under Ricci flow with curvature constraints.
method Proving a constant ε exists such that if a solution splits as a product at time 0 and has bounded curvature, it splits for all time.
result A constant ε exists depending on dimension such that if a solution splits as a product at time 0 and has curvature bounded by ε/t, it splits for all time.
A new model prices assets considering market microstructure effects.
problem Including market microstructure effects in dynamic asset pricing.
method Discrete binary tree model with history-dependent underlying security prices.
result The model preserves historical price dynamics and is market-complete, arbitrage-free.
We show uniqueness of Ricci flows starting at a surface of uniformly negative curvature, with the assumption that the flows become complete instantaneously. Together with the more general existence result proved in [10], this settles the issue of well-posedness in this class.
We prove a general existence result for instantaneously complete Ricci flows starting at an arbitrary Riemannian surface which may be incomplete and may have unbounded curvature. We give an explicit formula for the maximal existence time, and describe the asymptotic behaviour in most cases.
We use a first-order energy quantity to prove a strengthened statement of uniqueness for the Ricci flow. One consequence of this statement is that if a complete solution on a noncompact manifold has uniformly bounded Ricci curvature, then its sectional curvature will remain bounded for a short time if it is bounded ini…
Paper explores arbitrage and CAPM in continuous time.
problem Understanding arbitrage and CAPM in continuous time.
method Analyzes instantaneous arbitrage and its relation to CAPM.
result Arbitrage and CAPM arguments differ in assumptions about the market portfolio.
New framework IDOL identifies latent causal processes with instantaneous relations from time series data.
problem Identifying latent causal processes with instantaneous relations from time series data.
method Sparse influence constraint and variational inference architecture with sparsity regularization.
result Our method can identify latent causal processes with instantaneous relations.
New formula for instantaneous frequency in unbalanced systems.
problem Estimating frequency in unbalanced electrical systems.
method Utilizes affine differential geometry to link frequency and voltage derivatives.
result Proposes a new formula for instantaneous frequency estimation.
Arbitrage strategyq-fin.GN
An arbitrage strategy allows a financial agent to make certain profit out of nothing, i.e., out of zero initial investment. This has to be disallowed on economic basis if the market is in equilibrium state, as opportunities for riskless profit would result in an instantaneous movement of prices of certain financial ins…
iCITRIS learns causal variables from interactive systems with instantaneous effects.
problem Identifying causal variables from temporal sequences with instantaneous effects.
method iCITRIS method for causal representation learning that handles instantaneous effects in intervened temporal sequences.
result iCITRIS accurately identifies causal variables and their causal graph from three interactive system datasets.
Aggregation distorts causal discovery results but recovery is possible with partial linearity or prior.
problem Understanding how temporal aggregation affects causal discovery in aggregated data.
method Functional consistency and conditional independence consistency methods.
result Causal discovery results may be distorted by aggregation, but recovery is possible with certain conditions.
Study compares Fourier estimators to mitigate asynchrony effects in finance.
problem Impact of asynchrony on instantaneous financial estimates.
method Comparison of Malliavin-Mancino and Cuchiero-Teichmann estimators.
result Malliavin-Mancino estimator produces more stable estimates under asynchrony.
This work completes Chern-Ricci flow on complex manifolds with incomplete data.
problem Existence and behavior of Chern-Ricci flows on complex manifolds.
method Analyzes the flow and potential flow on complex manifolds with incomplete initial data.
result Obtains existence results for Chern-Ricci flows and Kähler-Einstein metrics.
Study gap phenomenon in flat manifolds with Ricci curvature.
problem Understanding curvature decay in flat manifolds.
method Construct solutions to Yamabe flow and analyze curvature decay.
result If curvature decays quickly, manifold must be flat.
Paper revises power theory using classical mechanics concepts.
problem Clarifying instantaneous power definitions for circuit elements.
method Defines power using classical mechanics concepts like velocity and momentum.
result General and compact expression for inductance, capacitance, and resistance powers.
Instantaneous volatility estimated from traded volume and spread.
problem Estimating market volatility accurately and quickly.
method Developed a new market invariant linking volatility, traded volume, spread, and order book volume. Used this invariant for instantaneous volatility estimation.
result Instantaneous volatility estimation reproduces realised volatility better than GARCH(1,1) prediction.
Study cryptocurrency price dynamics using adaptive EMD and spectral analysis.
problem Analyze the time-varying volatility of cryptocurrency prices.
method Adaptive complementary ensemble empirical mode decomposition (ACE-EMD) and Hilbert spectral analysis.
result Reveal the properties of various timescales in cryptocurrency price dynamics.
Modeling continuous movement of entities in latent space for interaction timing.
problem Analyzing timing and frequency of instantaneous interactions.
method Latent position model with continuous trajectories.
result Individual trajectories estimated from interaction data.
We study hedging and pricing of unattainable contingent claims in a non-Markovian regime-switching financial model. Our financial market consists of a bank account and a risky asset whose dynamics are driven by a Brownian motion and a multivariate counting process with stochastic intensities. The interest rate, drift, …
A new stochastic volatility model with quadratic drift prevents moment explosions and preserves stock price martingale property.
problem Avoiding moment explosions and preserving stock price martingale property in stochastic volatility models.
method Introduces a one-factor stochastic volatility model with quadratic drift and a linear dispersion function, showing that the quadratic term is crucial.
result The model prevents moment explosions and preserves the martingale property of the stock price process.
Extends option pricing model to incorporate market factor dynamics.
problem Option pricing models need to account for market influencing factors.
method Extended Kim-Stoyanov-Rachev-Fabozzi model using invariance principles.
result New binomial model for complete markets with log-return dynamics.
Collective behaviours taking place in financial markets reveal strongly correlated states especially during a crisis period. A natural hypothesis is that trend reversals are also driven by mutual influences between the different stock exchanges. Using a maximum entropy approach, we find coordinated behaviour during tre…
The paper proves a new discrete Laplacian for 3D meshes and shows its superiority over primal construction.
problem Developing a more accurate discrete Laplacian for 3D meshes.
method Proves the Euler-Lagrange equation for the Dirichlet energy using the associated discrete Laplacian of the dual construction.
result The associated discrete Laplacian is optimal in compared to the primal construction.
Study optimal execution in a transient price impact model with multiple traders.
problem Optimal execution among multiple traders with transient price impact.
method Analyzed -player optimal execution games in an Obizhaeva--Wang model with and without regularization. Derived equilibrium solutions and explained their behavior.
result Existence of equilibrium restored with a specific time-dependent cost on block trades, and equilibrium is tractable.
Estimates chirp signal frequencies using probabilistic models.
problem Estimating instantaneous frequencies of chirp signals when true forms are unknown.
method Non-linear Gaussian processes and stochastic filters/smothers for posterior estimation.
result The method outperforms state-of-the-art methods on synthetic and real-world datasets.
A new principle minimizes residual and introduces momentum to improve PDE solution dynamics.
problem Ill-conditioning in Dirac-Frenkel residual minimization leads to non-unique parameter dynamics.
method Introduces a history variable (momentum) to select better-conditioned parameter velocities, preserving residual minimization while promoting smooth parameter evolutions.
result The approach leads to increased robustness in singular and near-singular PDE solution regimes.
New model identifies regimes in non-stationary data.
problem Identifying latent regimes in non-stationary systems with instantaneous effects.
method Identifiable Markov Switching Models with exponential family noise.
result Established identifiability of latent regimes and causal structures.
Unified framework for optimal liquidation with small market impact and semimartingale strategies.
problem Optimal liquidation under small market impact and portfolio liquidation.
method Semimartingale strategies and convergence results for BSDEs with singular terminal conditions.
result Unified framework for embedding two common liquidation models and microscopic foundation for semimartingale strategies.
To convert standard Brownian motion into a positive process, Geometric Brownian motion (GBM) is widely used. We generalize this positive process by introducing an asymmetry parameter which describes the instantaneous volatility whenever the process reaches a new low. For our new process, …
An average instantaneous cross-correlation function is introduced to quantify the interaction of the financial market of a specific time. Based on the daily data of the American and Chinese stock markets, memory effect of the average instantaneous cross-correlations is investigated over different price return time inte…
Paper revisits five IF paradoxes using differential geometry.
problem Five paradoxes of Instantaneous Frequency in three-phase systems.
method Geometric interpretation of frequency to explain IF paradoxes.
result Revisits and explains five IF paradoxes through a common framework.
Valuation of Mortality Risk via the Instantaneous Sharpe Ratio: Applications to Life Annuitiesq-fin.PR
We develop a theory for valuing non-diversifiable mortality risk in an incomplete market. We do this by assuming that the company issuing a mortality-contingent claim requires compensation for this risk in the form of a pre-specified instantaneous Sharpe ratio. We apply our method to value life annuities. One result of…
We use a continuous version of the standard deviation premium principle for pricing in incomplete equity markets by assuming that the investor issuing an unhedgeable derivative security requires compensation for this risk in the form of a pre-specified instantaneous Sharpe ratio. First, we apply our method to price opt…
Financial Time Series Analysis and Forecasting with HHT Feature Generation and Machine Learningq-fin.CP
HHT feature generation enhances financial time series forecasting.
problem Forecasting nonstationary financial time series.
method CEEMD and HHT for decomposition, machine learning integration.
result HHT-enhanced models outperform traditional models in forecasting.
This paper introduces a new metric, ULI, for RL that ensures both cumulative and instantaneous performance.
problem High-stakes applications require RL algorithms to avoid playing bad policies.
method Introduces uniform last-iterate (ULI) guarantee, a stronger metric capturing both cumulative and instantaneous performance.
result ULI directly implies near-optimal cumulative performance across various metrics, but not the other way around.
Study shows gaps in Bitcoin order book are linked to returns but only in the short term.
problem Understanding the relationship between gaps and returns in Bitcoin order books.
method Examined the dynamics of gaps and returns in a Bitcoin order book without considering long-term causation.
result The causal relationship between gaps and returns is limited to instantaneous causation.
Causal inference uses observations to infer the causal structure of the data generating system. We study a class of functional models that we call Time Series Models with Independent Noise (TiMINo). These models require independent residual time series, whereas traditional methods like Granger causality exploit the var…
A multi-time scale non-Gaussian model of stock returnscond-mat.other
We propose a stochastic process for stock movements that, with just one source of Brownian noise, has an instantaneous volatility that rises from a type of statistical feedback across many time scales. This results in a stationary non-Gaussian process which captures many features observed in time series of real stock r…
Study shows past market trends reduce or increase correlations between futures contracts.
problem Estimating and managing risk in non-stationary futures markets.
method Applied Principal Regression Analysis (PRA) to quantify past market movements' effect on correlations.
result Past up or down 10-day trends reduce or increase instantaneous correlations, respectively.
This paper is concerned with the estimation of the volatility process in a stochastic volatility model of the following form: , where denotes the log-price and is a càdlàg semi-martingale. In the spirit of a series of recent works on the estimation of the cumulated volatility, we here focus …
Given a completely arbitrary surface, whether or not it has bounded curvature, or even whether or not it is complete, there exists an instantaneously complete Ricci flow evolution of that surface that exists for a specific amount of time [GT11]. In the case that the underlying Riemann surface supports a hyperbolic metr…
We develop a theory for pricing non-diversifiable mortality risk in an incomplete market. We do this by assuming that the company issuing a mortality-contingent claim requires compensation for this risk in the form of a pre-specified instantaneous Sharpe ratio. We prove that our ensuing valuation formula satisfies a nu…
The paper models term structures under volatility uncertainty using G-Brownian motion.
problem Modeling term structures with volatility uncertainty.
method Modeling instantaneous forward rates as a diffusion process driven by G-Brownian motion.
result Derives a sufficient condition for the absence of arbitrage under volatility uncertainty.
The proposed model modifies option pricing formulas for the basic case of log-normal probability distribution providing correspondence to formulated criteria of efficiency and completeness. The model is self-calibrating by historic volatility data; it maintains the constant expected value at maturity of the hedged inst…
New model shows VIX futures are more expensive than local volatility model suggests.
problem VIX futures pricing under local volatility model is incorrect.
method Developed a continuous stochastic volatility model to show VIX futures are more expensive than local volatility model.
result Inversion of convex ordering between local and stochastic variances observed in SPX market for short maturities.