A locally-built, LLM-digested index of recent arXiv papers in quant finance, geometry/topology, and statistical ML — keyword search served straight from SQLite on this machine.
Neural IVP solves IVPs with neural networks, overcoming scaling and conditioning issues.
The paper examines the neural tangent kernel for PINNs solving general PDEs and finds convergence conditions.
Bayesian methods solve complex nonlinear PDEs efficiently.
In his 1954 paper about the initial value problem for 2D hyperbolic nonlinear PDEs, P. Lax declared that he had "a strong reason to believe" that there must exist a well-defined class of "not genuinely nonlinear" nonlinear PDEs. In 1978 G. Boillat coined the term "completely exceptional" to denote it. In the case of $2…
We consider the framework proposed by Burgard and Kjaer (2011) that derives the PDE which governs the price of an option including bilateral counterparty risk and funding. We extend this work by relaxing the assumption of absence of transaction costs in the hedging portfolio by proposing a cost proportional to the amou…
New PDE systems generalize Hawking mass monotonicity.
This is an elementary introduction to exterior differential systems motivated by two examples: minimal submanifolds and the isometric embedding problem. The two main goals of the lectures are: 1. To explain how to find an appropriate geometric setting for studying a given system of pde. 2. To explain the Cartan algorit…
We consider an integro-differential equation derived from a system of coupled parabolic PDE and an ODE which describes an European option pricing with liquidity shocks. We study the well-posedness and prove comparison principle for the corresponding initial value problem.
This paper includes an original self contained proof of well-posedness of an initial-boundary value problem involving a non-local parabolic PDE which naturally arises in the study of derivative pricing in a generalized market model. We call this market model a semi-Markov modulated market. Although a wellposedness resu…
This paper includes a proof of well-posedness of an initial-boundary value problem involving a system of degenerate non-local parabolic PDE which naturally arises in the study of derivative pricing in a generalized market model. In a semi-Markov modulated GBM model the locally risk minimizing price function satisfies a…
The paper proves well-posedness of nonlocal PDEs related to stochastic control problems.
Finite-gap solutions approximate jets of initial data for certain BKM systems.
The paper presents a PDE method for xVA incorporation in financial derivatives.
New machine learning methods solve complex PDEs with improved accuracy.
The paper develops a new approach to solve vector-valued PDEs on manifolds with minimal regularity.
Structured CNN designed using the prior information of problems potentially improves efficiency over conventional CNNs in various tasks in solving PDEs and inverse problems in signal processing. This paper introduces BNet2, a simplified Butterfly-Net and inline with the conventional CNN. Moreover, a Fourier transform i…
This work is focused on the solvability of initial-boundary value problems for degenerate parabolic partial differential equations that arise in the pricing of Asian options, and on the investigation of differential and certain qualitative properties of solutions of such equations. The generalized solvability for such …
Study Lipschitz regularity for manifold-constrained ROF model on curved surfaces.
Automated PDE discovery from multiple noisy experiments.
We derive a backward and forward nonlinear PDEs that govern the implied volatility of a contingent claim whenever the latter is well-defined. This would include at least any contingent claim written on a positive stock price whose payoff at a possibly random time is convex. We also discuss suitable initial and boundary…
MSLs use parallelizable root-finding for efficient ODE and PDE solutions.
New ADANNs improve PDE approximations.
Study on PDEs in Heston model with unique solution and convergence proof.
Neural-PDE learns PDEs from data using LSTM, outperforming traditional methods.
Deep learning for HJB PDEs using synthetic data and residual minimization.
Solves probabilistic Lambert problem connecting astrodynamics with optimal mass transport.
Our goal is to resolve a problem proposed by Fernholz and Karatzas [On optimal arbitrage (2008) Columbia Univ.]: to characterize the minimum amount of initial capital with which an investor can beat the market portfolio with a certain probability, as a function of the market configuration and time to maturity. We show …
In this paper we study the reductions of evolutionary PDEs on the manifold of the stationary points of time--dependent symmetries. In particular we describe how that the finite dimensional Hamiltonian structure of the reduced system is obtained from the Hamiltonian structure of the initial PDE and we construct the time…
SCaSML improves PDE solvers by correcting errors efficiently.
Tensor Neural Networks solve high-dimensional PDEs for financial pricing.
We provide an asymptotic expansion of the value function of a multidimensional utility maximization problem from consumption with small non-linear price impact. In our model cross-impacts between assets are allowed. In the limit for small price impact, we determine the asymptotic expansion of the value function around …
Paper designs Poisson integrators using machine learning.
Center manifold analysis can be used in order to investigate the stability of the stationary solutions of various PDEs. This can be done by considering the PDE as an ODE between certain Banach spaces and linearising about the stationary solution. Here we investigate the volume preserving mean curvature flow using such …
Study of Killing spinor-valued forms and their integrability conditions.
In this paper, we present an initial attempt to learn evolution PDEs from data. Inspired by the latest development of neural network designs in deep learning, we propose a new feed-forward deep network, called PDE-Net, to fulfill two objectives at the same time: to accurately predict dynamics of complex systems and to …
In this paper, a standard PDE for the pricing of arithmetic average strike Asian call option is presented. A Crank-Nicolson Implicit Method and a Higher Order Compact finite difference scheme for this pricing problem is derived. Both these schemes were implemented for various values of risk free rate and volatility. Th…
Physics-informed WNO learns PDE solutions without labeled data.
Efficiently optimizes hyperparameters for PDE and inverse problems using Gaussian processes.
Study shows neural networks learn low frequencies first, proposing solutions.
The class of non-rigid registration methods proposed in the framework of PDE-constrained Large Deformation Diffeomorphic Metric Mapping is a particularly interesting family of physically meaningful diffeomorphic registration methods. PDE-constrained LDDMM methods are formulated as constrained variational problems, wher…
Study on stability of geodesic maps in non-isotropic manifolds.
FM4PDE learns PDE solutions from sparse data.
Establish C^{1,2} regularity of American value functions in Heston model
Meta-learning base distributions for efficient PDE solutions.
In this work, we present a machine learning approach for reducing the error when numerically solving time-dependent partial differential equations (PDE). We use a fully convolutional LSTM network to exploit the spatiotemporal dynamics of PDEs. The neural network serves to enhance finite-difference and finite-volume met…
EPGP priors solve linear PDEs from data.
Paper tackles DOCTR-L with SciPhy RL, solving neural PDEs from data.
A new method solves complex financial equations efficiently.