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 approach connects UQ in SciML to viscous HJ PDEs for efficient uncertainty quantification.
We consider some elementary aspects of the geometry of the space of probability measures endowed with Wasserstein distance. In such a setting, we discuss the various terms entering Perelman's shrinker entropy, and characterize two new monotonic functionals for the volume-normalized Ricci flow. One is obtained by a resc…
Paper designs Poisson integrators using machine learning.
Deep learning for HJB PDEs using synthetic data and residual minimization.
New method uses neural networks to solve complex PDEs from optimal control theory.
New approach uses PDE learning for faster RL fine-tuning.
PINNs struggle with data-to-PDE inconsistencies, limiting their accuracy.
Paper solves investment strategy optimization with deep learning.
The paper proves well-posedness of nonlocal PDEs related to stochastic control problems.
Deep learning method proves convergence for high-dimensional PDEs.
Develops neural network approximations for infinite-dimensional input-output maps.
In this paper, we extend the jump-diffusion model proposed by Davis and Lleo to include jumps in asset prices as well as valuation factors. The criterion, following earlier work by Bielecki, Pliska, Nagai and others, is risk-sensitive optimization (equivalent to maximizing the expected growth rate subject to a constrai…
We present a numerical model for the dynamics of thin viscous threads based on a discrete, Lagrangian formulation of the smooth equations. The model makes use of a condensed set of coordinates, called the centerline/spin representation: the kinematical constraints linking the centerline's tangent to the orientation of …
Random feature model approximates PDE solutions efficiently.
RandNet-Parareal uses neural networks to speed up time-parallel PDE solving.
On curved spaces, viscous fluids reach equilibrium quickly.
We propose a numerical method for solving high dimensional fully nonlinear partial differential equations (PDEs). Our algorithm estimates simultaneously by backward time induction the solution and its gradient by multi-layer neural networks, while the Hessian is approximated by automatic differentiation of the gradient…
A neural network approach solves optimal decumulation problems for pension plans.
This paper optimizes dividend payout rates with a drawdown constraint in a stochastic model.
RS-PINN uses randomized smoothing to speed up high-dimensional PDE simulations without sacrificing accuracy.
Neural networks solve high-dimensional HJB PDEs with asymptotic guarantees.
The paper calibrates SPX and VIX options using optimal transport.
Paper tackles DOCTR-L with SciPhy RL, solving neural PDEs from data.
A new method solves complex financial equations efficiently.
Paper explores solving HJB equations using neural networks.
Efficiently samples complex distributions using tensor train format.
We study an optimal investment/consumption problem in a model capturing market and credit risk dependencies. Stochastic factors drive both the default intensity and the volatility of the stocks in the portfolio. We use the martingale approach and analyze the recursive system of nonlinear Hamilton-Jacobi-Bellman equatio…
High-dimensional PDEs have been a longstanding computational challenge. We propose to solve high-dimensional PDEs by approximating the solution with a deep neural network which is trained to satisfy the differential operator, initial condition, and boundary conditions. Our algorithm is meshfree, which is key since mesh…
Quantum machine learning solves high-dimensional PDEs with lower variance and improved accuracy.
New method solves high-dimensional PDEs fast using physics-informed neural networks.
The paper analyzes thin-shell limits for viscous operators on Riemannian hypersurfaces.
The paper derives the QGS equations using stochastic central extensions.
In this paper, using Riemann-Lagrange geometrical methods, we construct a geometrical model on 1-jet spaces for the study of multi-time relativistic magnetized non-viscous plasma, characterized by a given energy-stress-momentum distinguished (d-) tensor. In that arena, we give the conservation laws and the continuity e…
Study optimal investment strategies with entropy regularization in volatile markets.
We propose a new algorithm for solving parabolic partial differential equations (PDEs) and backward stochastic differential equations (BSDEs) in high dimension, by making an analogy between the BSDE and reinforcement learning with the gradient of the solution playing the role of the policy function, and the loss functi…
This is the first in a series of papers in which we study an efficient approximation scheme for solving the Hamilton-Jacobi-Bellman equation for multi-dimensional problems in stochastic control theory. The method is a combination of a WKB style asymptotic expansion of the value function, which reduces the second order …
High-dimensional partial differential equations (PDE) appear in a number of models from the financial industry, such as in derivative pricing models, credit valuation adjustment (CVA) models, or portfolio optimization models. The PDEs in such applications are high-dimensional as the dimension corresponds to the number …
This paper considers a portfolio optimization problem in which asset prices are represented by SDEs driven by Brownian motion and a Poisson random measure, with drifts that are functions of an auxiliary diffusion factor process. The criterion, following earlier work by Bielecki, Pliska, Nagai and others, is risk-sensit…
We consider the problem of portfolio optimization in a simple incomplete market and under a general utility function. By working with the associated Hamilton-Jacobi-Bellman partial differential equation (HJB PDE), we obtain a closed-form formula for a trading strategy which approximates the optimal trading strategy whe…
Using a simple and well-motivated modification of the stress-energy tensor for a viscous fluid proposed by Lichnerowicz, we prove that Einstein's equations coupled to a relativistic version of the Navier-Stokes equations are well-posed in a suitable Gevrey class if the fluid is incompressible and irrotational. These la…
This study evaluates the importance of design of experiments for PINN in physics-informed deep learning.
The goal of the present work is twofold. First we prove the existence of an Hilbert Manifold structure on the space of immersed oriented closed surfaces with three derivatives in in an arbitrary sub-manifold of an euclidian space . Second, using this Hilbert manifold structure, we prove a lower semi co…
New sampling method uses stochastic interpolants and FBSDEs.
We derive a closed form portfolio optimization rule for an investor who is diffident about mean return and volatility estimates, and has a CRRA utility. The novelty is that confidence is here represented using ellipsoidal uncertainty sets for the drift, given a volatility realization. This specification affords a simpl…
Enhanced autoencoders improve ROMs for PDEs by capturing essential properties.
We report analytical results for the development of the viscous fingering instability in a cylindrical Hele-Shaw cell of radius a and thickness b. We derive a generalized version of Darcy's law in such cylindrical background, and find it recovers the usual Darcy's law for flow in flat, rectangular cells, with correctio…
In this paper, we study a semi-martingale optimal transport problem and its application to the calibration of Local-Stochastic Volatility (LSV) models. Rather than considering the classical constraints on marginal distributions at initial and final time, we optimise our cost function given the prices of a finite number…
Study indifference pricing for insurance policies in a regime-switching market model.