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.
Framework for energy markets using measure-valued processes.
Infinite dimensional measure-valued processes modeled as polynomial diffusions.
Study uses viscosity solutions to solve control problems involving measure-valued martingales.
Study on measure-valued CARMA processes in Banach spaces.
In this paper, we establish a fluid limit for a two--sided Markov order book model. Our main result states that in a certain asymptotic regime, a pair of measure-valued processes representing the "sell-side shape" and "buy-side shape" of an order book converges to a pair of deterministic measure-valued processes in a c…
We introduce a class of probability measure-valued diffusions, coined polynomial, of which the well-known Fleming--Viot process is a particular example. The defining property of finite dimensional polynomial processes considered by Cuchiero et al. (2012) and Filipovic and Larsson (2016) is transferred to this infinite …
This work optimizes bid strategies for online auctions using measure-valued optimization.
Optimal coupling among random vectors with known statistics and correlation structure found using minimum spanning tree over measure-valued vertices.
Active learning selects optimal measurement times for inferring continuous paths from sparse data.
A statistical description and model of individual healthcare expenditures in the US has been developed for measuring value in healthcare. We find evidence that healthcare expenditures are quantifiable as an infusion-diffusion process, which can be thought of intuitively as a steady change in the intensity of treatment …
We solve a complex Bayesian control problem with novel methods.
We introduce polynomial processes taking values in an arbitrary Banach space via their infinitesimal generator and the associated martingale problem. We obtain two representations of the (conditional) moments in terms of solutions of a system of ODEs on the truncated tensor algebra of dual respectively bidual s…
We obtain an explicit formula for the bilateral counterparty valuation adjustment of a credit default swaps portfolio referencing an asymptotically large number of entities. We perform the analysis under a doubly stochastic intensity framework, allowing for default correlation through a common jump process. The key ins…
The study examines convergence of stochastic processes on large graphs and adjacency matrices.
New guarantees for uniquely identifying transport maps and vector fields from finite measure-valued data.
In this paper we consider a mean-field model of interacting diffusions for the monetary reserves in which the reserves are subjected to a self- and cross-exciting shock. This is motivated by the financial acceleration and fire sales observed in the market. We derive a mean-field limit using a weak convergence analysis …
We study singular stochastic control of a two dimensional stochastic differential equation, where the first component is linear with random and unbounded coefficients. We derive existence of an optimal relaxed control and necessary conditions for optimality in the form of a mixed relaxed-singular maximum principle in a…
Develops a mathematical model for CLMM dynamics in DeFi.
We use GANs and signatures to approximate conditional laws in filtering and prediction of diffusion processes.
Optimal probability measure found for constrained stochastic processes.
We introduce the formalism of generalized Fourier transforms in the context of risk management. We develop a general framework to efficiently compute the most popular risk measures, Value-at-Risk and Expected Shortfall (also known as Conditional Value-at-Risk). The only ingredient required by our approach is the knowle…
A new diversification measure DQ derived from risk measures addresses limitations of existing indices.
This paper develops an asymptotic expansion technique in momentum space for stochastic filtering. It is shown that Fourier transformation combined with a polynomial-function approximation of the nonlinear terms gives a closed recursive system of ordinary differential equations (ODEs) for the relevant conditional distri…
In this paper we derive a second order approximation for an infinite dimensional limit order book model, in which the dynamics of the incoming order flow is allowed to depend on the current market price as well as on a volume indicator (e.g.~the volume standing at the top of the book). We study the fluctuations of the …
The aim of this note is to study the measure-valued Ricci tensor on smooth metric measure space with boundary, which is a generalization of Bakry-Emery's modified Ricci tensor on weighted Riemannian manifold. As an application, we offer a new approach to study curvature-dimension condition of smooth metric measure spac…
We consider an optimal stopping problem where a constraint is placed on the distribution of the stopping time. Reformulating the problem in terms of so-called measure-valued martingales allows us to transform the marginal constraint into an initial condition and view the problem as a stochastic control problem; we esta…
A new method warps inputs to learn nonstationary kernels efficiently.
Wasserstein GAN(WGAN) is a model that minimizes the Wasserstein distance between a data distribution and sample distribution. Recent studies have proposed stabilizing the training process for the WGAN and implementing the Lipschitz constraint. In this study, we prove the local stability of optimizing the simple gradien…
In this paper, we extend the DC Calculus introduced by Perelman on finite dimensional Alexandrov spaces with curvature bounded below. Among other things, our results allow us to define the Hessian and the Laplacian of DC functions (including distance functions as a particular instance) as a measure-valued tensor and a …
Paper introduces HRPCFD for efficient training of stochastic processes.
Unexpectedly, weighted Pareto variables are stochastically dominant.
Study improves accuracy of risk measures using advanced algorithms.
We model continuous-time information flows generated by a number of information sources that switch on and off at random times. By modulating a multi-dimensional Lévy random bridge over a random point field, our framework relates the discovery of relevant new information sources to jumps in conditional expectation mart…
Sharp heat kernel estimates on manifolds lead to solutions of the Parabolic Anderson model.
Recurring international financial crises have adverse socioeconomic effects and demand novel regulatory instruments or strategies for risk management and market stabilization. However, the complex web of market interactions often impedes rational decisions that would absolutely minimize the risk. Here we show that, for…
Generalized Lotka-Volterra (GLV) models extending the (70 year old) logistic equation to stochastic systems consisting of a multitude of competing auto-catalytic components lead to power distribution laws of the (100 year old) Pareto-Zipf type. In particular, when applied to economic systems, GLV leads to power laws in…
Conditional forecasts of risk measures play an important role in internal risk management of financial institutions as well as in regulatory capital calculations. In order to assess forecasting performance of a risk measurement procedure, risk measure forecasts are compared to the realized financial losses over a perio…
This paper examines the precision of estimators of Quantile-Based Risk Measures (Value at Risk, Expected Shortfall, Spectral Risk Measures). It first addresses the question of how to estimate the precision of these estimators, and proposes a Monte Carlo method that is free of some of the limitations of existing approac…
We present a framework for analyzing the exact dynamics of a class of online learning algorithms in the high-dimensional scaling limit. Our results are applied to two concrete examples: online regularized linear regression and principal component analysis. As the ambient dimension tends to infinity, and with proper tim…
We analyze the dynamics of an online algorithm for independent component analysis in the high-dimensional scaling limit. As the ambient dimension tends to infinity, and with proper time scaling, we show that the time-varying joint empirical measure of the target feature vector and the estimates provided by the algorith…
Quantum Portfolios of quantum algorithms encoded on qbits have recently been reported. In this paper a discussion of the continuous variables version of quantum portfolios is presented. A risk neutral valuation model for options dependent on the measured values of the observables, analogous to the traditional Black-Sch…
Study on membranes under confinement, proving existence and regularity of minimizers.
In this paper we study time-consistent risk measures for returns that are given by a GARCH(1,1) model. We present a construction of risk measures based on their static counterparts that overcomes the lack of time-consistency. We then study in detail our construction for the risk measures Value-at-Risk (VaR) and Average…
Paper characterizes star-shaped risk measures and their properties.
When society maintains a competitive system to promote an abstract goal, competition by necessity relies on imperfect proxy measures. For instance profit is used to measure value to consumers, patient volumes to measure hospital performance, or the Journal Impact Factor to measure scientific value. Here we note that \t…
We study the feasibility and noise sensitivity of portfolio optimization under some downside risk measures (Value-at-Risk, Expected Shortfall, and semivariance) when they are estimated by fitting a parametric distribution on a finite sample of asset returns. We find that the existence of the optimum is a probabilistic …
The paper explores capital allocation using Euler formula with VaR and ES, revealing non-monotonicity and providing estimation methods.
Bayesian optimization speeds up parameter reconstruction in optical nano-metrology.