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.
Study Brownian motion on Grassmann manifold using matrix stochastic calculus.
Teaches matrix calculus for machine learning and optimization.
Simplified calculus for semimartingales makes complex transformations easier.
This paper gives new concentration inequalities for the spectral norm of a wide class of matrix martingales in continuous time. These results extend previously established Freedman and Bernstein inequalities for series of random matrices to the class of continuous time processes. Our analysis relies on a new supermarti…
Derives optimal control conditions using calculus of variations.
Quantum calculus models stock liquidity issues.
Study on stochastic mean curvature flow on networks using Ito calculus.
The thesis examines stochastic calculus in option pricing with logistic models and numerical methods.
The article models illiquid stocks using quantum calculus with asymptotic methods.
In this article we present an intrinsec construction of foliated Brownian motion via stochastic calculus adapted to foliation. The stochastic approach together with a proposed foliated vector calculus provide a natural method to work on harmonic measures. Other results include a decomposition of the Laplacian in terms …
In this paper we construct the Differential calculus on the Hopf Group Coalgebra introduced by Turaev [10]. We proved that the concepts introduced by S.L.Woronowicz in constructing Differential calculus on Hopf Compact Matrix Pseudogroups (Quantum Groups)[7] can be adapted to serve again in our construction.
We revisit the theory of Discrete Exterior Calculus (DEC) in 2D for general triangulations, relying only on Vector Calculus and Matrix Algebra. We present DEC numerical solutions of the Poisson equation and compare them against those found using the Finite Element Method with linear elements (FEML).
In the framework of risk management, for the study of the sensitivity of pricing and hedging in stochastic financial models to changes of parameters and to perturbations of the stock prices, we propose an error calculus which is an extension of the Malliavin calculus based on Dirichlet forms. Although useful also in ph…
We provide a proof of backpropagation algorithm in matrix notation.
Optimizes reinsurance and investment strategies to minimize ruin probability.
In order to study the geometry of interest rates market dynamics, Malliavin, Mancino and Recchioni [A non-parametric calibration of the HJM geometry: an application of Itô calculus to financial statistics, {\it Japanese Journal of Mathematics}, 2, pp.55--77, 2007] introduced a scheme, which is based on the Fourier Seri…
This study introduces computation of option sensitivities (Greeks) using the Malliavin calculus under the assumption that the underlying asset and interest rate both evolve from a stochastic volatility model and a stochastic interest rate model, respectively. Therefore, it integrates the recent developments in the Mall…
The paper provides an efficient method to price path-dependent derivatives using multiscale stochastic volatility models.
We analyze quantum Yang-Mills theory on using a novel discretization method based on an algebraic analogue of stochastic calculus. Such an analogue involves working with "Gaussian" free fields whose covariance matrix is indefinite rather than positive definite. Specifically, we work with Lie-algebra valu…
Paper develops methods for solving complex stochastic equations using Malliavin calculus.
This paper is an attempt to explain all the matrix calculus you need in order to understand the training of deep neural networks. We assume no math knowledge beyond what you learned in calculus 1, and provide links to help you refresh the necessary math where needed. Note that you do not need to understand this materia…
The paper introduces a simple way of recording and manipulating general stochastic processes without explicit reference to a probability measure. In the new calculus, operations traditionally presented in a measure-specific way are instead captured by tracing the behaviour of jumps (also when no jumps are physically pr…
Derives Black-Scholes model without stochastic calculus or PDEs.
The aim of these notes is to relate covariant stochastic integration in a vector bundle (as in Norris \cite{Norris}) with the usual Stratonovich calculus via the connector $\K:TE \rightarrow E$ (cf. e.g. Paterson \cite{Paterson} or Poor \cite{Poor}) which carries the connection dependence.
The differential calculus on the quantum supergroup GL was introduced by Schmidke {\it et al}. (1990 {\it Z. Phys. C} {\bf 48} 249). We construct a differential calculus on the quantum supergroup GL in a different way and we obtain its quantum superalgebra. The main structures are derived without an…
Operator calculus for population-based optimization provides a unified framework for analyzing convergence of various methods.
The paper challenges the notion that asset return doesn't affect Black-Scholes-Merton model.
The Goeritz matrix of a link is obtained from the Jacobian matrix of a modified Dehn presentation associated to a diagram using Fox's free differential calculus. When the diagram is special the Seifert matrix can also be determined from the presentation.
Study short-term behavior of up-and-in barrier options using Malliavin calculus.
A new algorithm solves high-dimensional nonlinear BSDEs efficiently.
A non-commutative differential calculus on the -superplane is presented via a contraction of the -superplane. An R-matrix which satisfies both ungraded and graded Yang-Baxter equations is obtained and a new deformation of the dimensional classical phase space (the super-Heisenberg algebra) is introduced.
Enhancing the Black-Scholes model with Lévy processes and Malliavin calculus
The extremely useful method of Malliavin calculus has not yet gained adequate popularity because of the complicated analytic apparatus of this method. The author attempts here to propose a simplified algebraic formalism similar to Malliavin calculus, but based on the notion of creation-annihilation operators instead of…
Simplified Khovanov-Rozansky calculus for bipartite knots.
Researchers compute Greeks for rough Volterra SV models using Malliavin calculus.
New integration theory on topological spaces, including fractals.
Schrödinger bridge solved with Weyl calculus for quadratic state cost.
We present new stochastic differential equations, that are more general and simpler than the existing Ito-based stochastic differential equations. As an example, we apply our approach to the investment (portfolio) model.
The book explores stochastic areas and heat kernels on manifolds.
Researchers develop explicit approximations for European put options in stochastic volatility models.
The paper simplifies calculus for semimartingales using multiplicative compensation.
Formula for option pricing in a stochastic volatility model with jumps.
Paper defines multi-dimensional fractional Brownian motion under volatility uncertainty.
This paper uses Malliavin calculus to price and compute delta of financial derivatives in jump-diffusion models.
This paper describes the algorithms, features and implementation of PyDEC, a Python library for computations related to the discretization of exterior calculus. PyDEC facilitates inquiry into both physical problems on manifolds as well as purely topological problems on abstract complexes. We describe efficient algorith…
Develops a new calculus for stochastic processes with occupation flows.
We derive a numerical method for Darcy flow, hence also for Poisson's equation in mixed (first order) form, based on discrete exterior calculus (DEC). Exterior calculus is a generalization of vector calculus to smooth manifolds and DEC is one of its discretizations on simplicial complexes such as triangle and tetrahedr…
Optimizes shapes in uncertain Navier-Stokes flow problems.