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.
New methods solve SPDEs for financial derivative pricing.
The paper develops methods to price options under rough volatility models using BSPDEs.
We link SVEs to SPDEs and derive Kolmogorov equations for singular kernels.
We establish existence, uniqueness and regularity of solution results for a class of backward stochastic partial differential equations with singular terminal condition. The equation describes the value function of non-Markovian stochastic optimal control problem in which the terminal state of the controlled process is…
New method for dynamic valuation in markets with random endowments.
We study a constrained optimal control problem with possibly degenerate coefficients arising in models of optimal portfolio liquidation under market impact. The coefficients can be random in which case the value function is described by a degenerate backward stochastic partial differential equation (BSPDE) with singula…
In Bender and Dokuchaev (2013), we studied a control problem related to swing option pricing in a general non-Markovian setting. The main result there shows that the value process of this control problem can be uniquely characterized in terms of a first order backward SPDE and a pathwise differential inclusion. In the …
The purpose of this paper relies on the study of long term yield curves modeling. Inspired by the economic litterature, it provides a financial interpretation of the Ramsey rule that links discount rate and marginal utility of aggregate optimal consumption. For such a long maturity modelization, the possibility of adju…
Backward stochastic partial differential equations of parabolic type in bounded domains are studied in the setting where the coercivity condition is not necessary satisfied and the equation can be degenerate. Some generalized solutions based on the representation theorem are suggested. In addition to problems with a st…
Unified approach solves Kyle model with dynamic information.
Novel framework discovers SPDEs from limited data.
The paper examines conditions for stochastic invariance of cones in SPDEs with jumps.
Improved Gaussian process inference for spatio-temporal data.
Conservative SPDEs emerge from fluctuating SGD dynamics in neural networks.
Deep learning approximates SPDE solutions from noise trajectories.
Neural networks solve SPDEs using Wiener chaos expansion.
Bayesian nonparametric models get better posterior estimates via SPDE methods.
A new method uses SPDEs to efficiently model random fields on complex domains.
New graph kernels capture spatio-temporal interactions.
Adaptive learning of SPDE solutions using score-based diffusion models.
We consider systems of diffusion processes ("particles") interacting through their ranks (also referred to as "rank-based models" in the mathematical finance literature). We show that, as the number of particles becomes large, the process of fluctuations of the empirical cumulative distribution functions converges to t…
In this article, we propose a Milstein finite difference scheme for a stochastic partial differential equation (SPDE) describing a large particle system. We show, by means of Fourier analysis, that the discretisation on an unbounded domain is convergent of first order in the timestep and second order in the spatial gri…
SON learns SPDE solutions and uncertainty from noisy data.
Paper improves CDO calibration using Magnus Expansion and Deep Learning.
We propose a dynamic mean field model for `systemic risk' in large financial systems, which we derive from a system of interacting diffusions on the positive half-line with an absorbing boundary at the origin. These diffusions represent the distances-to-default of financial institutions and absorption at zero correspon…
Study well-posedness of SPDE on Riemannian manifolds with rough initial conditions.
Exchange uses incentives to optimize limit order book dynamics.
Derives new equations for stochastic volatility models.
Model for high-frequency trading with rough volatility.
Neural architecture improves geophysical data assimilation with uncertainty quantification.
We consider a stochastic model for the dynamics of the two-sided limit order book (LOB). Our model is flexible enough to allow for a dependence of the price dynamics on volumes. For the joint dynamics of best bid and ask prices and the standing buy and sell volume densities, we derive a functional limit theorem, which …
We prove a law of large numbers for the loss from default and use it for approximating the distribution of the loss from default in large, potentially heterogenous portfolios. The density of the limiting measure is shown to solve a non-linear SPDE, and the moments of the limiting measure are shown to satisfy an infinit…
We prove a maximum principle for mild solutions to stochastic evolution equations with (locally) Lipschitz coefficients and Wiener noise on weighted spaces. As an application, we provide sufficient conditions for the positivity of forward rates in the Heath-Jarrow-Morton model, considering the associated Musiela …
We consider an SPDE description of a large portfolio limit model where the underlying asset prices evolve according to certain stochastic volatility models with default upon hitting a lower barrier. The asset prices and their volatilities are correlated via systemic Brownian motions, and the resulting SPDE is defined o…
Motivated by a zero-intelligence approach, the aim of this paper is to connect the microscopic (discrete price and volume), mesoscopic (discrete price and continuous volume) and macroscopic (continuous price and volume) frameworks for the modelling of limit order books, with a view to providing a natural probabilistic …
The study optimizes Gaussian process approximations for finite-rank models.
Derives new equations for volatility models and option pricing.
New deep learning method approximates Benes filter model.
Paper presents a new backward deep BSDE method for solving nonlinear FBSDE problems.
Approximating Gaussian Whittle-Matern Fields over Well-Centered Triangulations of Riemannian Manifolds
Unified framework models multiple financial and insurance term structures.
In this paper, we study the evolving behaviors of the first eigenvalue of Laplace-Beltrami operator under the normalized backward Ricci flow, construct various quantities which are monotonic under the backward Ricci flow and get upper and lower bounds. We prove that in cases where the backward Ricci flow converges to a…
PASTIS method selects simple models from noisy data.
State-of-the-art computer codes for simulating real physical systems are often characterized by a vast number of input parameters. Performing uncertainty quantification (UQ) tasks with Monte Carlo (MC) methods is almost always infeasible because of the need to perform hundreds of thousands or even millions of forward m…
The study introduces backward baselines to distinguish past prediction from future prediction in machine learning models.
The paper extends NUP representations to factor graphs for better estimation.
Study proves existence of equilibrium in incomplete economies with discontinuous volatility.
Scalar dynamic risk measures for univariate positions in continuous time are commonly represented as backward stochastic differential equations. In the multivariate setting, dynamic risk measures have been defined and studied as families of set-valued functionals in the recent literature. There are two possible extensi…