Paper extends Brownian bridge with random length and pinning point for financial modeling.
problem Modeling financial information flow with uncertainty in pinning point.
method Introduced an extension of Brownian bridge with random length and pinning point, derived formulae for conditional expectations.
result The extended Brownian bridge fails to be Markovian if pinning point distribution is absolutely continuous.
The paper optimizes trading strategies for assets modeled by a randomized Brownian bridge.
problem Optimizing trading strategies for assets with uninformative noise and unknown terminal prices.
method Modeling asset price evolution with an exponential randomized Brownian bridge and solving for optimal trading strategies numerically.
result Disconnected continuation/exercise regions appear under certain prior distributions.
ABBA creates a new symbolic time series representation based on Brownian bridge.
problem Representing time series data in a compact, symbolic form.
method Adaptive polygonal chain approximation followed by mean-based clustering.
result ABBA outperforms other representations in preserving time series shape information.
Paper calculates when companies or states will default based on information flow.
problem Determining the timing of bankruptcy in information-based models.
method Explicit computation of compensator for a totally inaccessible stopping time.
result Explicit computation of the time of bankruptcy for inaccessible stopping times.
The issue of giving an explicit description of the flow of information concerning the time of bankruptcy of a company (or a state) arriving on the market is tackled by defining a bridge process starting from zero and conditioned to be equal to zero when the default occurs. This enables to catch some empirical facts on …
Optimizes selling bonds with non-negative prices using a Brownian bridge model.
problem Maximizing the expected value of an exponential gain function on a Brownian bridge.
method Develops pathwise properties of the Brownian bridge and uses martingale methods of optimal stopping theory.
result Solves the stopping problem for the exponential of a Brownian bridge.
Effective dimensionality reduction improves accuracy and reduces costs in estimating option Greeks.
problem Estimating Greeks for barrier and arithmetic average Asian options.
method Global sensitivity analysis, Chebyshev interpolation, conditional pathwise method, randomized Quasi Monte Carlo, Brownian bridge discretization, importance sampling.
result Reduced effective dimensionality enhances convergence rate and accuracy of randomized Quasi Monte Carlo integration.
New unbiased methods for generating stochastic bridges with given extrema.
problem Generating unbiased stochastic bridges with a specified extremum.
method Comparison and generalization of two algorithms for Brownian bridges to other diffusions, and application to Ornstein-Uhlenbeck and unconstrained processes.
result Generalization of unbiased generation methods to other diffusions and application to various processes.
Modeling financial information flows using random switches.
problem Understanding how new information sources affect financial markets.
method Modeling continuous-time information flows with random switches and Lévy bridges.
result The model captures complex information dynamics and can price financial options.
We prove an integration by parts formula for the probability measure induced by the semi-classical Riemmanian Brownian bridge over a manifold with a pole.
FDBM models use fractional Brownian motion to model complex stochastic processes.
problem Capturing memory effects and long-range dependencies in stochastic processes.
method Developed a generative diffusion bridge framework using a Markovian approximation of fractional Brownian motion.
result FDBM outperforms standard models in predicting future states and unpaired data translation.
Dynamic Black-Litterman integrates expert views with portfolio optimization over varying time horizons.
problem Incorporating expert views with varying horizons in portfolio optimization.
method Exploiting graphical structure, deriving conditional distribution of asset returns, and using affine factor models.
result Explicit expression for optimal dynamic investment policy and hedging demand analysis.
We study optimal double stopping problems driven by a Brownian bridge. The objective is to maximize the expected spread between the payoffs achieved at the two stopping times. We study several cases where the solutions can be solved explicitly by strategies of threshold type.
Optimizes American option exercise timing with discounted Brownian bridge model.
problem Optimizing American option exercise timing under special market conditions.
method Modeling terminal price as a Brownian bridge with future information disclosure and discount factor inclusion.
result Characterization and numerical computation of optimal stopping boundary with discount factor.
Extends martingale Schrödinger bridge to arbitrary dimensions and characterizes it.
problem Tackles the martingale Schrödinger bridge in arbitrary dimensions.
method Identifies continuous-time counterpart and relates to variational problems.
result Continuous martingale Schrödinger bridge coincides with Föllmer martingale in irreducible case.
The information-based asset-pricing framework of Brody, Hughston and Macrina (BHM) is extended to include a wider class of models for market information. In the BHM framework, each asset is associated with a collection of random cash flows. The price of the asset is the sum of the discounted conditional expectations of…
I prove that every adapted Brownian bridge on a geodesically complete connected Riemannian manifold is a semimartingale including its terminal time, without any further assumptions on the geometry. In particular, it follows that every such process can be horizontally lifted to a smooth principal fiber bundle with conne…
New SV models calibrated to market instruments using Schrodinger bridge approach.
problem Creating calibrated Stochastic Volatility Models to market instruments.
method Building a new class of SV models using Schrodinger bridge approach, with instantaneous volatility not modified.
result Models differ from local SV models and can be interpreted as martingale Schrodinger bridges.
Extends diffusion-based Schrödinger bridge models to handle time-dependent potentials.
problem Approximating optimal transport dynamics between two boundary distributions with a twisted Brownian motion reference.
method Introduces Twisted Schrödinger Bridge Matching (TSBM) using the Iterative Markovian Fitting (IMF) paradigm, incorporating a gradient-dependent bridge-matching loss.
result Improves trajectory inference across high-dimensional settings, including crowd navigation and single-cell data.
New pricing model uses variance-gamma process for financial assets.
problem Traditional pricing models need improvement for complex financial assets.
method Developed a new class of models based on variance-gamma process.
result The new model can price a variety of financial assets effectively.
Geodesic walks converge to Brownian motion on Finsler manifolds.
problem Understanding random walks on Finsler manifolds.
method Analyzing convergence of geodesic random walks to diffusion processes.
result The Brownian motion on a Riemannian metric is a key result.
New method generates synthetic time series paths with more flexibility.
problem Restrictions in generating synthetic paths using Brownian reference.
method Introduces Triangular-Reference Schrödinger Bridges (TR-SBTS) for time series generation.
result Generates synthetic paths with more flexibility in stochastic volatility and correlated noise.
Researchers define a limit for fractional Brownian motion as Hurst parameter approaches zero.
problem Defining a limit for fractional Brownian motion with zero Hurst parameter.
method Developed a Gaussian random distribution and log-correlated random field as limits.
result Fractional Brownian motion converges to a Gaussian random distribution when Hurst parameter approaches zero.
Extensions of Brownian motion to singular surfaces are studied.
problem Diffusion across singularities on surfaces.
method One-parameter family of Grushin-type singularities, heat crossing analysis, isometry group respect, Bessel processes.
result Complete description and classification of diffusions for various singularity cases.
The Brownian bridge serves as a physics-informed prior for solving the Poisson equation.
problem Reconstructing physical fields from limited and noisy data with known governing equations.
method Formalizing inverse problems via Bayesian inference in function spaces using a Brownian bridge Gaussian process.
result The Brownian bridge Gaussian process can be viewed as a physics-constrained prior for the Poisson equation, allowing for a fully Bayesian framework.
Study random walks on sub-Riemannian manifolds using retractions.
problem Modeling random walks on sub-Riemannian manifolds.
method Use retractions to approximate normal geodesics and study convergence to Brownian motion.
result Convergence of geodesic random walks defined with different connections.
Paper develops a new method for calculating the probability density of a fractional SABR model.
problem Lack of probability density calculations for lognormal fractional SABR model.
method Bridge representation in Fourier space, small time asymptotic expansion, large deviations principle derivation.
result Developed a method to calculate the probability density of fractional SABR model.
Innovative extensions to option pricing models using asymmetric Brownian motion and random walk approaches.
problem Capturing empirical phenomena like return skewness, heavy tails, and volatility asymmetry in option pricing models.
method Developing the Geometric Asymmetric Brownian Motion (GABM) within the Bachelier--Black--Scholes--Merton framework.
result Deriving closed-form option pricing formulas and a discrete-time binomial tree algorithm that converges to the GABM limit.
An efficient conditioning technique, the so-called Brownian Bridge simulation, has previously been applied to eliminate pricing bias that arises in applications of the standard discrete-time Monte Carlo method to evaluate options written on the continuous-time extrema of an underlying asset. It is based on the simple a…
This paper provides guarantees for DFM models using KL divergence.
problem Ensuring generative models match target distributions efficiently.
method Using KL divergence and Brownian motion bridge for generative models.
result Non-asymptotic guarantees for DFM models under specific conditions.
The paper shows how particle movement on a manifold's grid approximates Brownian motion and heat diffusion.
problem Understanding particle movement on curved spaces.
method Analyzing symmetric exclusion process on random grids approximating a Riemannian manifold.
result Empirical density field converges to heat equation solution on the manifold.
Deep learning solves PDEs with boundary conditions for barrier options.
problem Solving PDEs with boundary conditions for barrier options.
method Employing deep learning to approximate solutions of the PDE with boundary conditions.
result Deep learning can solve PDEs with boundary conditions for barrier options.
Random hyperbolic surfaces with punctures converge to the Brownian sphere.
problem Understanding the geometry of random hyperbolic surfaces with punctures.
method Rescaling and encoding via plane trees with continuous labels.
result Rescaled random hyperbolic surfaces converge to the Brownian sphere.
A generalized bridge is the law of a stochastic process that is conditioned on N linear functionals of its path. We consider two types of representations of such bridges: orthogonal and canonical. The orthogonal representation is constructed from the entire path of the underlying process. Thus, future knowledge of the …
New SDEs use G-Brownian motion, extending mean-field models.
problem Extending mean-field models to new types of stochastic processes.
method Introduced G-SDEs with coefficients dependent on current state and solution as random variable. result Validated new SDE framework for complex stochastic systems.
New method identifies drift and diffusivity from SDE marginals.
problem Challenging task to identify drift and diffusion from SDE population dynamics.
method Proposes nn-APPEX, a Schrodinger Bridge-based inference method.
result Gradient-flow drift and Brownian diffusivity jointly identifiable from marginals.
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…
Study investigates ruin probability with random premiums and risky investments.
problem Ruin probability with random premiums and risky investments.
method Laplace transform applied to a model with geometric Brownian motion.
result Asymptotic behavior of ruin probability for large initial capital values.
Study refracted skew Brownian motion, find densities and asymptotics.
problem Modeling and analyzing refracted skew Brownian motion.
method Perturbation approach to find potential densities, transition density, and asymptotic behaviors.
result Expressions and asymptotic behaviors of refracted skew Brownian motion.
The article calculates the most-likely path for Asian option pricing in local volatility models.
problem Approximating the price of Asian options in local volatility models.
method Path-integral approach using Brownian bridge and Laplace asymptotic formula.
result The most-likely path (MLP) is found to approximate the option price in the limit of small sampling time.
In this note, we derive a new logarithmic Sobolev inequality for the heat kernel on the Heisenberg group. The proof is inspired from the historical method of Leonard Gross with the Central Limit Theorem for a random walk. Here the non commutative nature of the increments produces a new gradient which naturally involves…
Proves CLT for Brownian paths on pinched negative curvature manifolds.
problem Distribution of Brownian paths on pinched negative curvature manifolds.
method Proof of central limit theorem for distances and Green functions.
result Central limit theorem holds for Brownian paths in pinched negative curvature.
We show that a random link defined by random bridge splitting is hyperbolic with asymptotic probability 1.
Paper solves fractional Brownian motion using Laplace transforms.
problem Fractional Brownian motion and its applications.
method Non-analytic solution via Laplace transform.
result Transition probability density function derived for fractional Brownian motion.
Invariance principle proved for lifted geodesic walks on Riemannian submersions.
problem Proving convergence to horizontal Brownian motion for lifted geodesic walks.
method Appropriate conditions on geodesic random walks' speed; proving invariance principle.
result Convergence to horizontal Brownian motion for lifted geodesic walks.
We propose a novel algorithm which allows to sample paths from an underlying price process in a local volatility model and to achieve a substantial variance reduction when pricing exotic options. The new algorithm relies on the construction of a discrete multinomial tree. The crucial feature of our approach is that -- …
Global approximation for piecewise linear paths via signatures.
problem Global approximation theorems for piecewise linear paths.
method Using signatures of piecewise linear paths and their density in Lp-norms. result Linear functionals of signatures are dense in Lp-norms under an integrability condition. Unified treatment of eigenvalue processes using Riemannian geometry.
problem Eigenvalue processes in various settings.
method Riemannian submersion and gradient flow of isospectral orbits.
result Eigenvalue processes are projections of Brownian motion through Riemannian submersions.