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.
Unified kernel framework extends to stochastic systems, improving numerical stability.
The paper develops a Feynman-Kac formula for perturbations of order ≤ 1 in noncommutative geometry.
We prove existence, regularity and a Feynman-Kač representation formula of the strong solution to the free boundary problem arising in the financial problem of the pricing of the American Asian option with arithmetic average.
Study analyzes derivative-free loss method for solving PDEs and fluid problems.
This paper models short rates with jumps using PDEs.
This is an introduction to Wiener measure and the Feynman-Kac formula on general Riemannian manifolds for Riemannian geometers with little or no background in stochastics. We explain the construction of Wiener measure based on the heat kernel in full detail and we prove the Feynman-Kac formula for Schrödinger operators…
The paper develops methods to price and hedge options in path-dependent stock models.
This study quantifies systemic importance in global banks using a continuous framework that amplifies localized shocks.
The paper generalizes Feynman-Kac formula for volatility uncertainty.
We prove Feynman-Kac formulas for solutions to elliptic and parabolic boundary value and obstacle problems associated with a general Markov diffusion process. Our diffusion model covers several popular stochastic volatility models, such as the Heston model, the CEV model and the SABR model, which are widely used as ass…
We prove Bismut-type formulae for the first and second derivatives of a Feynman-Kac semigroup on a complete Riemannian manifold. We derive local estimates and give bounds on the logarithmic derivatives of the integral kernel. Stationary solutions are also considered. The arguments are based on local martingales, althou…
The challenge to fruitfully merge state-of-the-art techniques from mathematical finance and numerical analysis has inspired researchers to develop fast deterministic option pricing methods. As a result, highly efficient algorithms to compute option prices in Lévy models by solving partial integro differential equations…
New methods solve SPDEs for financial derivative pricing.
New method improves training of PINNs for PDEs by adding noisy supervision terms.
Study indifference pricing for insurance policies in a regime-switching market model.
FKEE estimates expectations without samples, using diffusion bridges and PINNs.
New method recovers BSDE from financial data without ergodicity.
We prove a Feynman-Kac formula for differential forms satisfying absolute boundary conditions on Riemannian manifolds with boundary and of bounded geometry. We use this to construct harmonic forms out of bounded ones on the universal cover of a compact Riemannian manifold whose geometry displays a positivity prop…
Functional-analytic method for stochastic parallel transport in bundles.
New method trains partial Bayesian neural networks efficiently.
New method steers protein design towards desired properties.
In this paper, we pursue the study of second order BSDEs with jumps (2BSDEJs for short) started in our accompanying paper [15]. We prove existence of these equations by a direct method, thus providing complete wellposedness for 2BSDEJs. These equations are a natural candidate for the probabilistic interpretation of som…
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 …
Improved diffusion models using energy distillation and sequential Monte Carlo.
Novel filter uses deep BSDE for nonlinear density approximation.
Paper improves robustness and sparsity in adversarially trained DNNs.
Study on PDEs in Heston model with unique solution and convergence proof.
Exchange uses incentives to optimize limit order book dynamics.
We develop a new model for VIX derivatives with closed-form solutions.
Study heat profiles and eigenfunctions using Brownian motion.
Study of mean curvature flows with conical singularities using mathematical techniques.
In this paper, we investigate an optimal investment and consumption problem for an investor who trades in a Black--Scholes financial market with stochastic coefficients driven by a non-Gaussian Ornstein--Uhlenbeck process. We assume that an agent makes investment and consumption decisions based on a power utility funct…
Paper proves existence and uniqueness of solutions to nonlocal systems, generalizing stochastic game theory.
The paper provides gradient estimates for Neumann semigroups on manifolds with boundary under unbounded curvature conditions.
Using a suitable change of probability measure, we obtain a novel Poisson series representation for the arbitrage- free price process of vulnerable contingent claims in a regime-switching market driven by an underlying continuous- time Markov process. As a result of this representation, along with a short-time asymptot…
Stochastic delay differential equations (SDDE's) have been used for financial modeling. In this article, we study a SDDE obtained by the equation of a CIR process, with an additional fixed delay term in drift; in particular, we prove that there exists a unique strong solution (positive and integrable) which we call fix…
At first, we solve a problem of finding a risk-minimizing hedging strategy on a general market with ratings. Next, we find a solution to this problem on Markovian market with ratings on which prices are influenced by additional factors and rating, and behavior of this system is described by SDE driven by Wiener process…
We present a deep recurrent neural network architecture to solve a class of stochastic optimal control problems described by fully nonlinear Hamilton Jacobi Bellmanpartial differential equations. Such PDEs arise when one considers stochastic dynamics characterized by uncertainties that are additive and control multipli…
Study well-posedness of SPDE on Riemannian manifolds with rough initial conditions.
In this short note we outline a simple probabilistic proof of the Gauss-Bonnet formula for compact Riemannian manifolds with boundary, which adapts to this setting an argument due to Hsu \cite{Hs1,Hs2} in the closed case. The new technical ingredient is the Feynman-Kac formula for differential forms satisfying absolute…
ATSM are widely applied for pricing of bonds and interest rate derivatives but the consistency of ATSM when the short rate, r, is unbounded from below remains essentially an open question. First, the standard approach to ATSM uses the Feynman-Kac theorem which is easily applicable only when r is bounded from below. Sec…
We consider an optimal investment and consumption problem for a Black-Scholes financial market with stochastic coefficients driven by a diffusion process. We assume that an agent makes consumption and investment decisions based on CRRA utility functions. The dynamical programming approach leads to an investigation of t…
Study uses G-BSDEs to decompose pricing kernels under robust G-expectation.
Deep learning solves high-dimensional PDEs efficiently.
We introduce a deep neural network based method for solving a class of elliptic partial differential equations. We approximate the solution of the PDE with a deep neural network which is trained under the guidance of a probabilistic representation of the PDE in the spirit of the Feynman-Kac formula. The solution is giv…
AFT combines AIS, SMC, and NFs for better Monte Carlo estimates.
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…
Deep density methods improve filtering in high-dimensional systems.