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.
Proposes a new method to learn entire solution paths without discretization.
New algorithmic view of ℓ2 regularization using ODEs and path-following methods.
The paper develops methods to price and hedge options in path-dependent stock models.
Signature tensors uniquely identify ODE solutions.
For a variety of regularized optimization problems in machine learning, algorithms computing the entire solution path have been developed recently. Most of these methods are quadratic programs that are parameterized by a single parameter, as for example the Support Vector Machine (SVM). Solution path algorithms do not …
The paper explores moduli space of heterotic system using two deformation paths.
Develops a new solver for path-dependent PDEs using signature kernels.
We investigate the difficulties of training sparse neural networks and make new observations about optimization dynamics and the energy landscape within the sparse regime. Recent work of \citep{Gale2019, Liu2018} has shown that sparse ResNet-50 architectures trained on ImageNet-2012 dataset converge to solutions that a…
Extends tracking guarantees for time-varying variational inequalities.
New control theory for self-path-dependent problems solves unique constraints.
We give time-slicing path integral formulas for solutions to the heat equation corresponding to a self-adjoint Laplace type operator acting on sections of a vector bundle over a compact Riemannian manifold with boundary. More specifically, we show that such a solution can be approximated by integrals over finite-dimens…
New simulation approaches to evaluating path-dependent options without matrix inversion issues nor Euler bias are evaluated. They employ three main contributions: Stochastic approximation replaces regression in the LSM algorithm; Explicit weak solutions to stochastic differential equations are developed and applied to …
This study proposes an approach based on a perturbation technique to construct global solutions to dynamic stochastic general equilibrium models (DSGE). The main idea is to expand a solution in a series of powers of a small parameter scaling the uncertainty in the economy around a solution to the deterministic model, i…
New method uses LSTM and signature theory to solve complex financial PDEs.
The study examines insurance demand under rough volatility and path-dependent shocks.
In this paper, we recover sparse signals from their noisy linear measurements by solving nonlinear differential inclusions, which is based on the notion of inverse scale space (ISS) developed in applied mathematics. Our goal here is to bring this idea to address a challenging problem in statistics, \emph{i.e.} finding …
Solves complex equation for specific geometric solitons.
Study path geometries with constant torsion and cone structures.
Convex clustering is a promising new approach to the classical problem of clustering, combining strong performance in empirical studies with rigorous theoretical foundations. Despite these advantages, convex clustering has not been widely adopted, due to its computationally intensive nature and its lack of compelling v…
The recently developed bag-of-paths (BoP) framework consists in setting a Gibbs-Boltzmann distribution on all feasible paths of a graph. This probability distribution favors short paths over long ones, with a free parameter (the temperature ) controlling the entropic level of the distribution. This formalism enables…
We consider a general path-dependent version of the hedging problem with price impact of Bouchard et al. (2019), in which a dual formulation for the super-hedging price is obtained by means of PDE arguments, in a Markovian setting and under strong regularity conditions. Using only probabilistic arguments, we prove, in …
Improved RL for knowledge graph reasoning with entity types.
We consider an infinite horizon portfolio problem with borrowing constraints, in which an agent receives labor income which adjusts to financial market shocks in a path dependent way. This path-dependency is the novelty of the model, and leads to an infinite dimensional stochastic optimal control problem. We solve the …
In recent years, we have established the iteration theory of the index for symplectic matrix paths and applied it to periodic solution problems of nonlinear Hamiltonian systems. This paper is a survey on these results.
In this paper, we introduce and develop the theory of semimartingale optimal transport in a path dependent setting. Instead of the classical constraints on marginal distributions, we consider a general framework of path dependent constraints. Duality results are established, representing the solution in terms of path d…
We consider the problem of path inference: given a path prefix, i.e., a partially observed sequence of nodes in a graph, we want to predict which nodes are in the missing suffix. In particular, we focus on natural paths occurring as a by-product of the interaction of an agent with a network---a driver on the transporta…
Develops a numerical scheme for solving path-dependent FBSDEs and PDEs.
In this work we establish the equivalence of algorithmic regularization and explicit convex penalization for generic convex losses. We introduce a geometric condition for the optimization path of a convex function, and show that if such a condition is satisfied, the optimization path of an iterative algorithm on the un…
Nested model averaging improves high-dimensional linear regression performance.
We provide theoretical analysis of the statistical and computational properties of penalized -estimators that can be formulated as the solution to a possibly nonconvex optimization problem. Many important estimators fall in this category, including least squares regression with nonconvex regularization, generalized …
In this paper, we extend the first-order asymptotics analysis of Fouque et al. to general path-dependent financial derivatives using Dupire's functional Ito calculus. The main conclusion is that the market group parameters calibrated to vanilla options can be used to price to the same order exotic, path-dependent deriv…
Let M be a compact Riemannian manifold without boundary and let H be a self-adjoint generalized Laplace operator acting on sections in a bundle over M. We give a path integral formula for the solution to the corresponding heat equation. This is based on approximating path space by finite dimensional spaces of geodesic …
We develop an iterative subsampling approach to improve the computational efficiency of our previous work on solution path clustering (SPC). The SPC method achieves clustering by concave regularization on the pairwise distances between cluster centers. This clustering method has the important capability to recognize no…
Solves complex Monge-Ampère equation for Kähler-Ricci solitons.
The notion of friendliness between trees first appeared in solution of Lando's problem on intersection of polyhedra in 3-space. A tree is friendly to a path graph if edges of the tree can be numbered so that for each k,s the path between the edges k and k+1 contains either both or none of the edges k+2s,k+2s+1. Theorem…
Deep learning improves probabilistic PPDE solution accuracy.
We derive a closed-form solution for the price of an average price as well as an average strike geometric Asian option, by making use of the path integral formulation. Our results are compared to a numerical Monte Carlo simulation. We also develop a pricing formula for an Asian option with a barrier on a control proces…
CoMPNetX uses neural networks to efficiently solve constrained motion planning problems.
We present a method for obtaining approximate solutions to the problem of optimal execution, based on a signature method. The framework is general, only requiring that the price process is a geometric rough path and the price impact function is a continuous function of the trading speed. Following an approximation of t…
New control methods improve dynamic measure transport paths.
The -1 norm based optimization is widely used in signal processing, especially in recent compressed sensing theory. This paper studies the solution path of the -1 norm penalized least-square problem, whose constrained form is known as Least Absolute Shrinkage and Selection Operator (LASSO). A solution path …
A new method for portfolio allocation in continuous-time markets.
With an eye toward understanding complexity control in deep learning, we study how infinitesimal regularization or gradient descent optimization lead to margin maximizing solutions in both homogeneous and non-homogeneous models, extending previous work that focused on infinitesimal regularization only in homogeneous mo…
Given a compact symplectic manifold , with integral symplectic form, we prequantize a certain class of functions on the path space for . The functions in question are induced by functions on . We apply our construction to study the symplectic structure on the solution space of Klein-Gordon equation.
This paper studies a class of nonMarkovian singular stochastic control problems, for which we provide a novel probabilistic representation. The solution of such control problem is proved to identify with the solution of a constrained BSDE, with dynamics associated to a non singular underlying forward process. Du…
The paper develops fair machine learning models using causal path-specific effects.
Path-dependent PDEs model VIX and Realised Variance options.
Framework for training stochastic spiking neural networks with rough signals.