arXiv research

Classifies domains critical for heat content and exit-time moments.

Study shows submanifolds can't be immersed in certain spaces.

We prove explicit upper and lower bounds for the $L^1$-moment spectra for the Brownian motion exit time from extrinsic metric balls of submanifolds $P^m$ in ambient Riemannian spaces $N^{n}$. We assume that $P$ and $N$ both have controlled radial curvatures (mean curvature and sectional curvature, respectively) as view…

We compute the first Dirichlet eigenvalue of a geodesic ball in a rotationally symmetric model space in terms of the moment spectrum for the Brownian motion exit times from the ball. This expression implies an estimate as exact as you want for the first Dirichlet eigenvalue of a geodesic ball in these rotationally symm…

Analyzes first exit times in a modified Barndorff-Nielsen and Shephard model.

New method controls mean exit time in stochastic systems using machine learning and quasipotential.

The purpose of this article is to compute the expected first exit times of Brownian motion from a variety of domains in the Euclidean plane and in the hyperbolic plane.

Developed policy gradient methods for stochastic control with exit time, outperforming traditional techniques in share repurchase pricing.

Study compares eigenvalues and moment spectra of geodesic balls in Riemannian manifolds.

Study uses LLMs to optimize VC exit timing after IPO.

Mean exit times concentrate near equators and minimal hypersurfaces in high dimensions.

We apply the theory of continuous time random walks to study some aspects of the extreme value problem applied to financial time series. We focus our attention on extreme times, specifically the mean exit time and the mean first-passage time. We set the general equations for these extremes and evaluate the mean exit ti…

This paper proposes and analyses a new multilevel Monte Carlo method for the estimation of mean exit times for multi-dimensional Brownian diffusions, and associated functionals which correspond to solutions to high-dimensional parabolic PDEs through the Feynman-Kac formula. In particular, it is proved that the complexi…

We study theoretical and empirical aspects of the mean exit time of financial time series. The theoretical modeling is done within the framework of continuous time random walk. We empirically verify that the mean exit time follows a quadratic scaling law and it has associated a pre-factor which is specific to the analy…

By appealing to renewal theory we determine the equations that the mean exit time of a continuous-time random walk with drift satisfies both when the present coincides with a jump instant or when it does not. Particular attention is paid to the corrections ensuing from the non-Markovian nature of the process. We show t…

The purpose of this note is to give details for an argument of Sullivan to construct eigenfunctions of the Laplacian on a Riemannian manifold using exit times of Brownian motion \cite{sullivanpos}. Let $X$ be a complete, simply connected Riemannian manifold of pinched negative sectional curvature. Let $λ_1 = λ_1(X) < 0…

Study examines strategic exit timing in uncertain competition.

The paper uses machine learning to compute rare event probabilities in stochastic systems.

Large deviation principles for multivariate stochastic volatility models.

We solve the escape problem for the Heston random diffusion model. We obtain exact expressions for the survival probability (which ammounts to solving the complete escape problem) as well as for the mean exit time. We also average the volatility in order to work out the problem for the return alone regardless volatilit…

We consider a new approach to portfolio selection in presence of transaction costs which allows to map the problem into one without costs. The proposed approach connects all the quantities of interest to exit times and probabilities to reach barriers. This leads to analytic results in the Wiener case and to directly me…

Investors optimize liquid staking decisions in LSP and AMM protocols.

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…

Investigations of inverse statistics (a concept borrowed from turbulence) in stock markets, exemplified with filtered Dow Jones Industrial Average, S&P 500, and NASDAQ, have uncovered a novel stylized fact that the distribution of exit time follows a power law $p(τ_ρ) \sim τρ^{-α}$ with $α\approx 1.5$ at large $τ_ρ$ an…

Paper analyzes venture capital exit decisions under inconsistent preferences.

The inversion formula for conservative multifractal measures was unveiled mathematically a decade ago, which is however not well tested in real complex systems. In this Letter, we propose to verify the inversion formula using high-frequency turbulent financial data. We construct conservative volatility measure based on…

Optimizes liquidity withdrawal timing for AMM LPs to balance fees and impermanent loss.

Given a sequence of convex functions $f_0, f_1, \ldots, f_T$, we study the problem of sampling from the Gibbs distribution $π_t \propto e^{-\sum_{k=0}^tf_k}$ for each epoch $t$ in an online manner. Interest in this problem derives from applications in machine learning, Bayesian statistics, and optimization where, rathe…

This paper investigates sufficient conditions for a Feynman-Kac functional up to an exit time to be the generalized viscosity solution of a Dirichlet problem. The key ingredient is to find out the continuity of exit operator under Skorokhod topology, which reveals the intrinsic connection between overfitting Dirichlet …

This paper is concerned with cost optimization of an insurance company. The surplus of the insurance company is modeled by a controlled regime switching diffusion, where the regime switching mechanism provides the fluctuations of the random environment. The goal is to find an optimal control that minimizes the total co…

New SDE model from machine learning optimization with unique stationary distribution.

Paper uses sparse learning to estimate quasi-potential and drift components in stochastic systems.

An intense research on financial market microstructure is presently in progress. Continuous time random walks (CTRWs) are general models capable to capture the small-scale properties that high frequency data series show. The use of CTRW models in the analysis of financial problems is quite recent and their potentials h…

In this paper we discuss the optimal liquidation over a finite time horizon until the exit time. The drift and diffusion terms of the asset price are general functions depending on all variables including control and market regime. There is also a local nonlinear transaction cost associated to the liquidation. The mode…

Study volatility models with rough paths, focusing on large deviations and option behavior.

Lewis and Mordecki have computed the Wiener-Hopf factorization of a Lévy process whose restriction on $]0,+\infty[$ of their Lévy measure has a rational Laplace transform. That allows to compute the distribution of $(X_t,\inf_{0\leq s\leq t}X_s)$. For the same class of Lévy processes, we compute the distribution of $ (…

We prove explicit upper and lower bounds for the torsional rigidity of extrinsic domains of submanifolds P^m with controlled radial mean curvature in ambient Riemannian manifolds N^n with a pole p and with sectional curvatures bounded from above and from below, respectively. These bounds are given in terms of the torsi…

A new method calculates fractional moments using the moment-generating function.

Study compares weak and homotopy moment maps in multisymplectic geometry.

For a GJR-GARCH specification with a generic innovation distribution we derive analytic expressions for the first four conditional moments of the forward and aggregated returns and variances. Moment for the most commonly used GARCH models are stated as special cases. We also the limits of these moments as the time hori…

Optimal timing strategy for mean-reverting price spreads.

This paper identifies and bounds ICE central moments using PO marginal central moments.

We tackle causal inference under conditional moment restrictions using importance weighting.

Revisits Lee's Moment Formula, relaxing moment assumptions for implied volatility.

Developed moment estimators for affine stochastic volatility models.

Stiefel-Whitney classes of moment-angle manifolds are trivial.

A new method for estimating causal parameters from observables reduces the need for finite moment conditions.

Introduces generalized moment maps for almost Hermitian settings.