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.
The paper connects higher order risk measures and stochastic dominance, showing their equivalence and integrating them with optimization.
Paper uses second-order differential geometry to study stochastic mechanics.
In this paper, we study stochastic non-convex optimization with non-convex random functions. Recent studies on non-convex optimization revolve around establishing second-order convergence, i.e., converging to a nearly second-order optimal stationary points. However, existing results on stochastic non-convex optimizatio…
Proposes new rule for ranking investment prospects over long horizons.
First-order method solves stochastic bilevel optimization with linear constraints.
New method for pricing options in stochastic volatility models.
New characterization of second-order stochastic dominance with applications in risk management.
New algorithm reduces regret in stochastic bandit convex optimization.
Paper proposes a second-order method for faster SVI convergence.
New method for zeroth-order stochastic gradient algorithms provides confidence intervals.
Exact second-order optimization for deep learning reduces computational cost and improves performance.
Using agent-based modelling, empirical evidence and physical ideas, such as the energy function and the fact that the phase space must have twice the dimension of the configuration space, we argue that the stochastic differential equations which describe the motion of financial prices with respect to real world probabi…
Expands learning paradigm to stochastic orders using Choquet-Toland distance and Variational Dominance Criterion.
We study a generalized family of stochastic orders, semiparametrized by a distortion function H, namely H-distorted stochastic dominance, which may determine a continuum of dominance relations from the first- to the second-order stochastic dominance (and beyond). Such a family is especially suitable for representing a …
New algorithm finds approximate stationary points in non-convex optimization.
New methods reduce constraint violations to certainty in stochastic optimization.
New method improves zeroth-order stochastic optimization with adaptive sampling.
Optimal algorithms for Riemannian optimization with reduced complexity.
New model estimates higher-order interactions in stochastic processes using lower-dimensional projections.
In this paper, we propose a new technique named \textit{Stochastic Path-Integrated Differential EstimatoR} (SPIDER), which can be used to track many deterministic quantities of interest with significantly reduced computational cost. We apply SPIDER to two tasks, namely the stochastic first-order and zeroth-order method…
We propose a new high-order alternating direction implicit (ADI) finite difference scheme for the solution of initial-boundary value problems of convection-diffusion type with mixed derivatives and non-constant coefficients, as they arise from stochastic volatility models in option pricing. Our approach combines differ…
We present a sparse grid high-order alternating direction implicit (ADI) scheme for option pricing in stochastic volatility models. The scheme is second-order in time and fourth-order in space. Numerical experiments confirm the computational efficiency gains achieved by the sparse grid combination technique.
We extend the scheme developed in B. Düring, A. Pitkin, "High-order compact finite difference scheme for option pricing in stochastic volatility jump models", 2019, to the so-called stochastic volatility with contemporaneous jumps (SVCJ) model, derived by Duffie, Pan and Singleton. The performance of the scheme is asse…
A new method speeds up quantum state estimation.
In this paper, we propose and analyze zeroth-order stochastic approximation algorithms for nonconvex and convex optimization, with a focus on addressing constrained optimization, high-dimensional setting and saddle-point avoiding. To handle constrained optimization, we first propose generalizations of the conditional g…
First-order stochastic methods are the state-of-the-art in large-scale machine learning optimization owing to efficient per-iteration complexity. Second-order methods, while able to provide faster convergence, have been much less explored due to the high cost of computing the second-order information. In this paper we …
A new method for pricing options with stochastic volatility and jumps.
A new notion of stochastic ordering is introduced to compare multivariate stochastic risk models with respect to extreme portfolio losses. In the framework of multivariate regular variation comparison criteria are derived in terms of ordering conditions on the spectral measures, which allows for analytical or numerical…
We introduce TrustVI, a fast second-order algorithm for black-box variational inference based on trust-region optimization and the reparameterization trick. At each iteration, TrustVI proposes and assesses a step based on minibatches of draws from the variational distribution. The algorithm provably converges to a stat…
AdaSub optimizes with second-order info in low-dims subspace.
Optimal trade execution in a fluctuating market with stochastic liquidity.
A new machine learning method solves high-dimensional Kolmogorov PDEs efficiently.
In this paper, we investigate the popular deep learning optimization routine, Adam, from the perspective of statistical moments. While Adam is an adaptive lower-order moment based (of the stochastic gradient) method, we propose an extension namely, HAdam, which uses higher order moments of the stochastic gradient. Our …
Study optimal strategies for unwinding uncertain order flows in financial trading desks.
The paper calculates option prices using Mellin transform for stochastic volatility models.
Paper improves stochastic bilevel optimization methods for highly-smooth problems.
We analyze stochastic gradient algorithms for optimizing nonconvex problems. In particular, our goal is to find local minima (second-order stationary points) instead of just finding first-order stationary points which may be some bad unstable saddle points. We show that a simple perturbed version of stochastic recursiv…
This study compares the largest claims from two insurance portfolios using stochastic orderings.
Two classes of methods have been proposed for escaping from saddle points with one using the second-order information carried by the Hessian and the other adding the noise into the first-order information. The existing analysis for algorithms using noise in the first-order information is quite involved and hides the es…
Solves risk minimization problem with SSD constraints.
We propose an analytically tractable class of models for the dynamics of a limit order book, described through a stochastic partial differential equation (SPDE) with multiplicative noise for the order book centered at the mid-price, along with stochastic dynamics for the mid-price which is consistent with the order flo…
Optimized method tackles convex optimization with heavy-tailed noise.
We present two new remarkably simple stochastic second-order methods for minimizing the average of a very large number of sufficiently smooth and strongly convex functions. The first is a stochastic variant of Newton's method (SN), and the second is a stochastic variant of cubically regularized Newton's method (SCN). W…
Unified approach for first-order methods with Markovian noise in stochastic optimization and variational inequalities.
Two algorithms solve nonconvex minimax problems with linear constraints, achieving complexity guarantees.
Study on convex ordering in stochastic control for swing contracts, proving value function convexity.
Recent advances in Bayesian learning with large-scale data have witnessed emergence of stochastic gradient MCMC algorithms (SG-MCMC), such as stochastic gradient Langevin dynamics (SGLD), stochastic gradient Hamiltonian MCMC (SGHMC), and the stochastic gradient thermostat. While finite-time convergence properties of th…
We derive a new high-order compact finite difference scheme for option pricing in stochastic volatility models. The scheme is fourth-order accurate in space and second-order accurate in time. Under some restrictions, theoretical results like unconditional stability in the sense of von Neumann are presented. Where the a…