The paper solves a complex option pricing model using finite elements.
problem Risk-Adjusted Pricing Methodology (RAPM) Black-Scholes model with transaction costs.
method Spatial finite element models based on P1 and/or P2 elements, combined with a Crank-Nicolson-type temporal scheme.
result Results compare favorably with finite difference methods in the literature.
Finite element method applied to Leland's model for option pricing with transaction costs.
problem Option pricing with transaction costs using Leland's model.
method Spatial finite element models based on P1 and/or P2 elements combined with a Crank-Nicolson-type temporal scheme.
result Results compare favorably with finite difference methods in the literature.
Proposes a new model for clustering with heavier tails.
problem Clustering with heavy-tailed data.
method Finite mixture of skewed sub-Gaussian stable distributions, maximum likelihood estimation, EM algorithm.
result The proposed model can robustly handle heavy-tailed data.
Empirical study compares finite- and infinite-width BNNs, revealing performance differences under model mismatch.
problem Comparing BNNs with different widths due to conflicting model properties and inference intractability.
method Empirical comparison of finite- and infinite-width BNNs, analyzing performance under model mismatch.
result Increasing width can hurt BNN performance when the model is mis-specified, and finite-width BNNs generalize better under model mismatch.
We evaluate the hedging performance of a high-order compact finite difference scheme from [4] for option pricing in Bates model. We compare the scheme's hedging performance to standard finite difference methods in different examples. We observe that the new scheme outperforms a standard, second-order central finite dif…
Privacy concerns have led to the development of privacy-preserving approaches for learning models from sensitive data. Yet, in practice, even models learned with privacy guarantees can inadvertently memorize unique training examples or leak sensitive features. To identify such privacy violations, existing model auditin…
Paper solves convertible bond valuation using finite elements with penalty method.
problem Valuation of convertible bonds under penalty TF model.
method Solves TF system of equations using P1 and P2 finite elements with penalty method.
result Numerical solutions compare favorably with finite difference method.
New algorithms improve spectral clustering for finite mixture models.
problem Issues with EM algorithm in spectral clustering.
method Spectral decomposition and non-parametric bootstrap sampling.
result Improved convergence and avoidance of poor solutions.
The paper studies multi-curve interest rate models and their consistency and finite-dimensional realizations.
problem Consistency and existence of finite-dimensional realizations for multi-curve interest rate models.
method Geometric approach, characterizing consistency and existence of finite-dimensional realizations for multi-curve models.
result Characterization of consistency and existence of finite-dimensional realizations for multi-curve models.
We derive a new high-order compact finite difference scheme for option pricing in stochastic volatility jump models, e.g. in Bates model. In such models the option price is determined as the solution of a partial integro-differential equation. The scheme is fourth order accurate in space and second order accurate in ti…
New method for pricing options in stochastic volatility models.
problem Pricing options in models with stochastic volatility.
method Time-adaptive, high-order compact finite difference scheme.
result Extends fourth-order multistep methods to stochastic volatility models.
New method estimates mixture model components efficiently.
problem Estimating the number of components in finite mixture models.
method Group-Sort-Fuse (GSF) procedure for simultaneous estimation of order and mixing measure.
result GSF achieves consistent estimation of true mixture order and n−1/2 convergence rate. Lie's third theorem proven for Lie ∞-algebras.
problem Integrating finite-type Lie ∞-algebras to Lie ∞-groups.
method Local minimal models for Kan simplicial manifolds.
result Every finite-type Lie ∞-algebra integrates to a finite-dimensional Lie ∞-group.
Let G be a word hyperbolic group in the sense of Gromov and P its associated Rips complex. We prove that the fixed point set PH is contractible for every finite subgroups H of G. This is the main ingredient for proving that P is a finite model for the universal space e.g. of proper actions. As a corollar…
Ghost points affect stability in finite difference schemes for diffusion equations.
problem Impact of ghost points on stability of finite difference schemes.
method Exploration of explicit Euler finite difference scheme with ghost points on diffusion equation.
result Stability of the scheme is affected by ghost points.
We present a finite-dimensional version of the quantum model for the stock market proposed in [C. Zhang and L. Huang, A quantum model for the stock market, Physica A 389(2010) 5769]. Our approach is an attempt to make this model consistent with the discrete nature of the stock price and is based on the mathematical for…
We investigate one-point reduction methods of finite topological spaces. These methods allow one to study homotopy theory of cell complexes by means of elementary moves of their finite models. We also introduce the notion of h-regular CW-complex, generalizing the concept of regular CW-complex, and prove that the h-regu…
Observing prices of European put and call options, we calibrate exponential Lévy models nonparametrically. We discuss the efficient implementation of the spectral estimation procedures for Lévy models of finite jump activity as well as for self-decomposable Lévy models. Based on finite sample variances, confidence inte…
The paper develops finite knot theory using ropelength-filtered Reidemeister graphs.
problem Understanding knot types in bounded ropelength sublevel spaces.
method Study thick representatives in bounded ropelength sublevel spaces through lifted Reidemeister graphs.
result Define characteristic Reidemeister patterns and finite recognition length.
Paper proposes MWDE for estimating finite location-scale mixtures.
problem Estimating finite location-scale mixtures using MLE is problematic.
method Investigates minimum Wasserstein distance estimators (MWDE).
result MWDE is consistent and provides a numerical solution.
Typically options with a path dependent payoff, such as Target Accumulation Redemption Note (TARN), are evaluated by a Monte Carlo method. This paper describes a finite difference scheme for pricing a TARN option. Key steps in the proposed scheme involve tracking of multiple one-dimensional finite difference solutions,…
Decomposition complexity for metric spaces was recently introduced by Guentner, Tessera, and Yu as a natural generalization of asymptotic dimension. We prove a vanishing result for the continuously controlled algebraic K-theory of bounded geometry metric spaces with finite decomposition complexity. This leads to a proo…
We study the finite-size effects in some scaling systems, and show that the finite number of agents N leads to a cut-off in the upper value of the Pareto law for the relative individual wealth. The exponent α of the Pareto law obtained in stochastic multiplicative market models is crucially affected by the fact that …
We show that the moment explosion time in the rough Heston model [El Euch, Rosenbaum 2016, arxiv:1609.02108] is finite if and only if it is finite for the classical Heston model. Upper and lower bounds for the explosion time are established, as well as an algorithm to compute the explosion time (under some restrictions…
New model-free DR-RL algorithm with finite sample complexity.
problem Limited model-free DR-RL methods with convergence guarantees or sample complexities.
method Integrates Multi-level Monte Carlo (MLMC) technique with threshold mechanism.
result First model-free DR-RL approach with finite sample complexity for total variation and Chi-square divergence.
A theory of finite type invariants for arbitrary compact oriented 3-manifolds is proposed, and illustrated through many examples arising from both classical and quantum topology. The theory is seen to be highly non-trivial even for manifolds with large first betti number, encompassing much of the complexity of Ohtsuki'…
Abstract: Geometrically reformulates estimation theory for finite-dimensional C*-algebras.
problem Estimation theory for finite-dimensional C*-algebras.
method Geometrical formulation of estimation theory.
result Derivation of Cramer-Rao and Helstrom bounds.
Theory captures feature learning effects in finite CNNs.
problem Feature learning in finite deep neural networks.
method Derive a self-consistent Gaussian Process theory.
result Good agreement with experiments and sharp transition between regimes.
Statistical finite elements use Langevin dynamics to efficiently handle uncertainty quantification.
problem Uncertainty quantification in finite element models with observed data.
method Langevin dynamics, unadjusted Langevin algorithm (ULA), for sampling posterior distributions.
result ULA provides a scalable and efficient method for characterizing the posterior distribution of statFEM models.
New result on finite gerbes simplifies classification of certain bundles.
problem Classifying finite-dimensional gerbes with torsion DD-class. method Proves torsion for a wide class of finite gerbes built from principal bundles.
result Finite gerbes built from finite-dimensional fibre bundles have torsion DD-class. A new method for pricing options with stochastic volatility and jumps.
problem Pricing options under stochastic volatility and jumps.
method Fourth-order compact finite-difference scheme with implicit-explicit Crank-Nicolson framework.
result The method achieves near-fourth-order spatial accuracy and up to two orders of magnitude lower runtime than quadratic finite elements.
Conditions of Stability for explicit finite difference scheme and some results of numerical analysis for a unified 2 factor model of structural and reduced form types for corporate bonds with fixed discrete coupon are provided. It seems to be difficult to get solution formula for PDE model which generalizes Agliardi's …
Study shows how numerical discretization affects reconstructions and parameter distributions in nano metrology.
problem Impact of numerical discretization on parameter reconstructions and model parameter distributions.
method Bayesian target vector optimization, finite element model, Gaussian process, stochastic machine learning surrogate models, Markov chain Monte Carlo sampler.
result Numerical discretization parameters impact the accuracy and distribution of reconstructed model parameters.
Extending BTZ models to complete hyperbolic surfaces.
problem Extending BTZ models to complete hyperbolic surfaces.
method Proving a parametrization result for globally hyperbolic Cauchy-maximal and Cauchy-compact locally Minkowski manifolds with extreme BTZ.
result The tangent bundle of the Teichmüller space parametrizes globally hyperbolic Cauchy-maximal and Cauchy-compact locally Minkowski manifolds with extreme BTZ.
This paper analyzes hedge errors in Black-Scholes models using finite difference techniques.
problem Accurate hedging strategies in dynamic market environments.
method Asymptotic approach and finite difference techniques.
result Reduction of hedge errors and enhancement of option pricing model robustness.
New algorithms minimize regret in SSP with optimal sparse updates.
problem Minimizing regret in Stochastic Shortest Path models.
method Implicit finite-horizon approximation for analysis, model-free and model-based algorithms developed.
result Minimax optimal regret for both model-free and model-based algorithms.
The study optimizes Gaussian process approximations for finite-rank models.
problem Posterior behavior of finite-rank approximations differs from parent GP priors.
method Locally supported basis expansions with dependent Gaussian coefficients.
result Finite-rank expansions inherit the same posterior contraction rate as parent GP priors.
In this paper we present a new Bayesian network model for classification that combines the naive-Bayes (NB) classifier and the finite-mixture (FM) classifier. The resulting classifier aims at relaxing the strong assumptions on which the two component models are based, in an attempt to improve on their classification pe…
Enhanced Black-Scholes model for option pricing with stochastic volatility and interest rate variability.
problem Improving option pricing accuracy in volatile financial markets.
method Extended Black-Scholes model using finite difference method and LSTM machine learning.
result Finite difference method outperforms LSTM in computational efficiency but not in accuracy.
Spatially constrained Gaussian mixture models reduce covariance complexity.
problem High dimensionality in finite mixture models for spatial data.
method Spatial covariance constraint with only four free parameters.
result Improves clustering of multi-way spatial data and inference of spatial patterns.
Cyclic coordinate descent identifies models in finite time and converges linearly.
problem Model identification in composite nonsmooth optimization problems.
method Cyclic coordinate descent for a wide class of functions.
result Explicit local linear convergence rates for coordinate descent.
The paper shows how to learn causal representations with few environments and finite samples.
problem Learning causal representations from limited data and environments.
method Explicit, finite-sample guarantees with a logarithmic number of interventions.
result Consistent recovery of latent causal graph, mixing matrix, and unknown intervention targets.
Project infinite time series graphs to finite marginal models using number theory.
problem Handling infinite time series graphs for causal inference.
method Projection method using number theory to find common ancestors in infinite graphs.
result Developed algorithm to project infinite graphs to finite marginal models.
The study explores finite quotients of 3-manifold groups and their existence and non-existence.
problem Does there exist a 3-manifold group with a specific finite quotient but not others?
method The approach combines group cohomology, topological results, and probabilistic methods.
result Proves existence and non-existence of 3-manifolds with certain finite quotients.
Paper applies subdiffusive dynamics to American and barrier options pricing.
problem Valuation of American and barrier options in subdiffusive financial models.
method Proposes weighted finite difference and Longstaff-Schwartz methods for valuation.
result Numerical valuation of American and barrier options demonstrated.
We identify linear models from nonlinear systems with initialization constraints.
problem Identifying linear models from nonlinear systems with initialization constraints.
method Multiple trajectories-based deterministic data acquisition algorithm followed by regularized least squares.
result We provide a finite sample error bound on the learned linearized dynamics.
TAMD prevents degeneracy in finite mixtures, offering strong guarantees but modest practical improvements.
problem Degeneracy in maximum likelihood estimation of finite mixtures.
method Transcendental regularization with analytic barrier functions.
result Strong theoretical guarantees (identifiability, consistency, robustness) but modest practical improvements.
Paper detects gradual changes in cluster structure using MC fusion.
problem Detecting gradual changes in cluster structure over time.
method MC fusion for multiple mixture numbers, examining MC transition.
result Accurately captures cluster structure during transitional periods.