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 for inferring, predicting, and estimating continuous-time, discrete-event processes.
Efficient deep policy gradient method for continuous-time control problems.
New insights into RL efficiency from managing time discretization.
Despite remarkable successes, Deep Reinforcement Learning (DRL) is not robust to hyperparameterization, implementation details, or small environment changes (Henderson et al. 2017, Zhang et al. 2018). Overcoming such sensitivity is key to making DRL applicable to real world problems. In this paper, we identify sensitiv…
In this introductory paper, we discuss how quantitative finance problems under some common risk factor dynamics for some common instruments and approaches can be formulated as time-continuous or time-discrete forward-backward stochastic differential equations (FBSDE) final-value or control problems, how these final val…
We propose a novel time discretization for the log-normal SABR model which is a popular stochastic volatility model that is widely used in financial practice. Our time discretization is a variant of the Euler-Maruyama scheme. We study its asymptotic properties in the limit of a large number of time steps under a certai…
We generalize the primal-dual methodology, which is popular in the pricing of early-exercise options, to a backward dynamic programming equation associated with time discretization schemes of (reflected) backward stochastic differential equations (BSDEs). Taking as an input some approximate solution of the backward dyn…
We constructively prove the existence of time-discrete consumption processes for stochastic money accounts that fulfill a pre-specified positively homogeneous projection property (PHPP) and let the account always be positive and exactly zero at the end. One possible example is consumption rates forming a martingale und…
In this research the technology of complex Markov chains is applied to predict financial time series. The main distinction of complex or high-order Markov Chains and simple first-order ones is the existing of aftereffect or memory. The technology proposes prediction with the hierarchy of time discretization intervals a…
Unified discrete diffusion for categorical data simplifies training and sampling.
Numerous empirical proofs indicate the adequacy of the time discrete auto-regressive stochastic volatility models introduced by Taylor in the description of the log-returns of financial assets. The pricing and hedging of contingent products that use these models for their underlying assets is a non-trivial exercise due…
The convolution method for the numerical solution of forward-backward stochastic differential equations (FBSDEs), introduced in [21], uses a uniform space grid. In this paper we utilize a tree-like spatial discretization that approximates the BSDE on the tree, so that no spatial interpolation procedure is necessary. In…
New simulation method simplifies Heston model with Poisson conditioning for better accuracy and efficiency.
Develops pathwise analysis for log-optimal portfolios using rough paths theory.
Study improves sampling efficiency of diffusion models using RL and PDEs.
Continuous time stochastic processes are useful models especially for financial and insurance purposes. The numerical simulation of such models is dependant of the time discrete discretization, of the parametric estimation and of the choice of a random number generator. The aim of this paper is to provide the tools for…
In this paper a simple, effective adaptation of Alternating Direction Implicit (ADI) time discretization schemes is proposed for the numerical pricing of American-style options under the Heston model via a partial differential complementarity problem. The stability and convergence of the new methods are extensively inv…
Deep reinforcement learning boosts commodities trading performance.
D2SRM solves complex PDEs using deep learning.
Improved convergence rates for MFLD in various gradient estimators.
Constructs approximate mean curvature flows for general varifolds.
Forward-Euler fails for simulating Wasserstein gradient flows with KL divergence.
We propose a numerical algorithm for backward stochastic differential equations based on time discretization and trigonometric wavelets. This method combines the effectiveness of Fourier-based methods and the simplicity of a wavelet-based formula, resulting in an algorithm that is both accurate and easy to implement. F…
Multi-stage financial decision optimization under uncertainty depends on a careful numerical approximation of the underlying stochastic process, which describes the future returns of the selected assets or asset categories. Various approaches towards an optimal generation of discrete-time, discrete-state approximations…
Continuous-time Q-learning theory developed for reinforcement learning.
Paper explores how Rectified Flow adapts to low-dimensional data.
New framework models time-uncertain point processes for better event prediction.
Develops unbiased estimation method using underdamped Langevin dynamics.
We study polygonal analogues of several moving boundary problems and their time discretization which preserves the constant area speed property. We establish various polygonal analogues of geometric formulas for moving boundaries and make use of the geometric formulas for our numerical scheme and its analysis of genera…
Continuous-time algorithms improve online learning performance.
New EOT solvers estimate both plans and maps efficiently.
We propose a new method for the numerical solution of backward stochastic differential equations (BSDEs) which finds its roots in Fourier analysis. The method consists of an Euler time discretization of the BSDE with certain conditional expectations expressed in terms of Fourier transforms and computed using the fast F…
Consider a discrete-time infinite horizon financial market model in which the logarithm of the stock price is a time discretization of a stochastic differential equation. Under conditions different from those given in a previous paper of ours, we prove the existence of investment opportunities producing an exponentiall…
Monte Carlo simulations of diffusion processes often introduce bias in the final result, due to time discretization. Using an auxiliary Poisson process, it is possible to run simulations which are unbiased. In this article, we propose such a Monte Carlo scheme which converges to the exact value. We manage to keep the s…
In this article we propose a novel approach to reduce the computational complexity of various approximation methods for pricing discrete time American options. Given a sequence of continuation values estimates corresponding to different levels of spatial approximation and time discretization, we propose a multi-level l…
New error bound for diffusion models without dimensionality constraints.
Market makers optimize trading with a new implicit scheme for complex inequalities.
PAGP uses physics-assisted Gaussian processes to solve and learn PDEs.
Hierarchical geodesic model for analyzing shapes on manifolds.
In this paper we investigate the effectiveness of Alternating Direction Implicit (ADI) time discretization schemes in the numerical solution of the three-dimensional Heston-Hull-White partial differential equation, which is semidiscretized by applying finite difference schemes on nonuniform spatial grids. We consider t…
SGLD proves geometric ergodicity via reflection coupling for nonconvex log-concave distributions.
Paper develops a continuous-time framework for financial markets without stochastic calculus.
We consider an investor facing a classical portfolio problem of optimal investment in a log-Brownian stock and a fixed-interest bond, but constrained to choose portfolio and consumption strategies that reduce a dynamic shortfall risk measure. For continuous- and discrete-time financial markets we investigate the loss i…
Improved sampling method using regularized Stein Variational Gradient Flow.
Continuous-time MBRL framework tackles control systems with Bayesian ODEs.
TriTPP models enable faster and more flexible event data modeling.
We present the MagNet, a neural network-based multi-agent interaction model to discover the governing dynamics and predict evolution of a complex multi-agent system from observations. We formulate a multi-agent system as a coupled non-linear network with a generic ordinary differential equation (ODE) based state evolut…
This article presents a finite element method (FEM) for a partial integro-differential equation (PIDE) to price two-asset options with underlying price processes modeled by an exponential Levy process. We provide a variational formulation in a weighted Sobolev space, and establish existence and uniqueness of the FEM-ba…