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 surveys mathematical results on filtration enlargement with financial examples.
Golden age of mathematical finance in the late 20th century.
Lean 4 library formalizes mathematical finance, verifying over 200 theorems.
Lean 4 library formalizes mathematical finance, verifying over 200 theorems.
Extends Itô's formula for path-dependent functions in finance.
Quantum computing promises new financial modeling.
We establish higher-order weighted Sobolev and Holder regularity for solutions to variational equations defined by the elliptic Heston operator, a linear second-order degenerate-elliptic operator arising in mathematical finance. Furthermore, given -smooth data, we prove -regularity of solutions up t…
This paper proposes a general duality framework for the problem of minimizing a convex integral functional over a space of stochastic processes adapted to a given filtration. The framework unifies many well-known duality frameworks from operations research and mathematical finance. The unification allows the extension …
Investigates the effects of nondominated sets of probability measures in robust models of finance.
This paper studies dynamic stochastic optimization problems parametrized by a random variable. Such problems arise in many applications in operations research and mathematical finance. We give sufficient conditions for the existence of solutions and the absence of a duality gap. Our proof uses extended dynamic programm…
Mathematical framework for differential machine learning in finance.
Quantum GAN improves volatility modeling in finance.
Quantum algorithms speed up financial model calculations.
Survey revisits Bachelier and Dupire, highlighting optimal transport's role.
New methods solve complex PDEs with mixed boundary conditions.
In this note we review the basic mathematical ideas used in finance in the language of modern physics. We focus on discrete time formalism, derive path integral and Green's function formulas for pricing. We also discuss various risk mitigation methods.
In mathematical finance a popular approach for pricing options under some Levy model is to consider underlying that follows a Poisson jump diffusion process. As it is well known this results in a partial integro-differential equation (PIDE) that usually does not allow an analytical solution while numerical solution bri…
Semi-static trading strategies make frequent appearances in mathematical finance, where dynamic trading in a liquid asset is combined with static buy-and-hold positions in options on that asset. We show that the space of outcomes of such strategies can have very poor closure properties when all European options for a f…
Unified approach to stochastic Volterra systems' deviations.
These are the lecture notes for the summer course given for 2018 Mathematical Finance Summer School at Shandong Unversity. It contains a brief introduction to the Kyle model and the related topics in filtering, enlargement of filtrations and Markov bridges.
The Heston stochastic volatility process, which is widely used as an asset price model in mathematical finance, is a paradigm for a degenerate diffusion process where the degeneracy in the diffusion coefficient is proportional to the square root of the distance to the boundary of the half-plane. The generator of this p…
Python module for RL trading in limit order books.
New integral transforms solve multilayer heat equations.
Optimizes leveraged staking strategies in decentralized finance.
The goal of this note is to illustrate the impact of a self-financing condition recently introduced by the authors. We present the analyses of two specific applications usually considered in more traditional models in financial mathematics. They include hedging European options with limit orders and the optimal behavio…
This paper examines the quantitative finance aspects of AMMs in decentralized finance.
Lévy driven term structure models have become an important subject in the mathematical finance literature. This paper provides a comprehensive analysis of the Lévy driven Heath-Jarrow-Morton type term structure equation. This includes a full proof of existence and uniqueness in particular, which seems to have been lack…
Develops a mathematical model for CLMM dynamics in DeFi.
Clarifies when solutions to stochastic PDEs stay near given subsets.
GANs analyzed for performance and training issues.
In mathematical Finance calculating the Greeks by Malliavin weights has proved to be a numerically satisfactory procedure for finite-dimensional Itô-diffusions. The existence of Malliavin weights relies on absolute continuity of laws of the projected diffusion process and a sufficiently regular density. In this article…
Unified treatment of CLTs for Lévy models across physics, finance, and econometrics.
We consider a specific type of nonlinear partial differential equations (PDE) that appear in mathematical finance as the result of solving some optimization problems. We review some existing in the literature examples of such problems, and discuss the properties of these PDEs. We also demonstrate how to solve them nume…
Study of Markov-modulated affine processes for richer models in finance.
Develops new techniques for learning from sequential data groups.
Since Hobson's seminal paper [D. Hobson: Robust hedging of the lookback option. In: Finance Stoch. (1998)] the connection between model-independent pricing and the Skorokhod embedding problem has been a driving force in robust finance. We establish a general pricing-hedging duality for financial derivatives which are s…
In this paper, we provide conditions which ensure that stochastic Lipschitz BSDEs admit Malliavin differentiable solutions. We investigate the problem of existence of densities for the first components of solutions to general path-dependent stochastic Lipschitz BSDEs and obtain results for the second components in part…
Recent progress in the field of artificial intelligence, machine learning and also in computer industry resulted in the ongoing boom of using these techniques as applied to solving complex tasks in both science and industry. Same is, of course, true for the financial industry and mathematical finance. In this paper we …
Extends inf-convolution to countable risk measures for risk sharing.
We give an exposition, following joint works with J.-C. Zambrini, of the link between Euclidean Quantum Mechanics, Bernstein processes and isovectors for the heat equation. A new application to Mathematical Finance is then discussed.
This short note aims to point out mistakes in one of the implications for Theorem 2.8 in Bayraktar and Yu [Mathematical Finance, 28 (2018), pp. 800-838], which weakens the statement of this theorem.
Mathematical study of excess growth rate connects info theory with finance.
NeuralChaos efficiently approximates complex stochastic processes.
New framework for managing medical risks using convex responses.
We review a numerical technique, referred to as the Transport-based Mesh-free Method (TMM), and we discuss its applications to mathematical finance. We recently introduced this method from a numerical standpoint and investigated the accuracy of integration formulas based on the Monte-Carlo methodology: quantitative err…
In this paper we use convolutional neural networks to find the Hölder exponent of simulated sample paths of the rBergomi model, a recently proposed stock price model used in mathematical finance. We contextualise this as a calibration problem, thereby providing a very practical and useful application.
New principles for collapsing law-invariant functionals to means, extending beyond convexity.
A very brief history of relative valuation in neoclassical finance since 1973 is presented, with attention to core currency issues for emerging economies. Price formation is considered in the context of hierarchical causality, with discussion focussed on identifying mathematical modelling challenges for robust and tran…