arXiv research

We develop methods to approximate derivatives for causal inference problems using data.

Proposes a new derivative concept for nonlinear DRO problems.

We do further investigation in a certain cosine function defined for smooth Minkowski spaces. We prove that such function is symmetric if and only if the referred space is Euclidean, and also that it can be given in terms of the Gateaux derivative of the norm. As an application we use it to study the ratio between the …

The paper optimizes regret using covariance between costs and decisions.

The importance of collateralization through the change of funding cost is now well recognized among practitioners. In this article, we have extended the previous studies of collateralized derivative pricing to more generic situation, that is asymmetric and imperfect collateralization with the associated counter party c…

The increasingly common use of neural network classifiers in industrial and social applications of image analysis has allowed impressive progress these last years. Such methods are however sensitive to algorithmic bias, i.e. to an under- or an over-representation of positive predictions or to higher prediction errors i…

We present a framework on how to hedge the interest rate sensitivity of liabilities discounted by an extrapolated yield curve. The framework is based on functional analysis in that we consider the extrapolated yield curve as a functional of an observed yield curve and use its Gâteaux variation to understand the sensiti…

Solves a game between brokers and informed traders using stochastic differential equations.

Study on helix curves and their Möbius energy asymptotics.

Improved similarity search in embeddings using InfoNCE loss.

This paper extends risk parity to continuous-time, solving risk budgeting problems.

In the paper, we study numerically the projections of the real exchange rate dynamics onto the string-like topology. Our approach is inspired by the contemporary movements in the string theory. The string map of data is defined here by the boundary conditions, characteristic length, real valued and the method of redist…

Recently, based on the idea of randomizing space theory, random convex analysis has been being developed in order to deal with the corresponding problems in random environments such as analysis of conditional convex risk measures and the related variational problems and optimization problems. Random convex analysis is …

Researchers found the Wigner derivative and its inverse are equal for spherical tetrahedra.

The paper shows objective derivatives are covariant derivatives on Riemannian metrics.

Computes derivatives of sections in vector bundles using Lie derivatives.

Paper proposes auction method for smart derivatives to avoid disputes.

Derivatives impact U.S. banking sector's systemic risk, but loan and leverage ratios are more significant.

This paper deals with the concept of curvature of framed space curves, their higher-order derivatives, variations, and co-rotational derivatives. We realize that parametrizing rotation tensor using the Gibbs vector is effective in deriving a closed form formula to obtain any order derivative of the curvature tensor as …

Schwarzian derivative connects to Euler-Lagrange equations in variational calculus.

Paper develops formulas for shape derivatives in wave scattering.

A simple theory of the covariant derivatives, deformed derivatives and relative covariant derivatives of multivector and multiform fields is presented using algebraic and analytical tools developed in previous papers.

Study compares Indian derivatives markets and finds NSE outperforming BSE.

Former physicists share insights on derivatives in interviews.

Introduces Darboux-Lie derivative for fiber bundles.

New derivations on diffeological spaces are not smooth, expanding tangent space definitions.

Develops derived differential geometry theory.

Derives spacetime regularity under specific curvature conditions.

Approximates derivative pricing under fractional stochastic volatility.

In this article, we combine replication pricing with expectation pricing for derivative trades that are partially collateralized by cash. The derivatives are replicated by underlying assets and cash, using repurchasing agreement (repo) and margining, which incur funding costs. We derive a partial differential equation …

We introduce and study a construction of higher derived brackets generated by a (not necessarily inner) derivation of a Lie superalgebra. Higher derived brackets generated by an element of a Lie superalgebra were introduced in our earlier work. Examples of higher derived brackets naturally appear in geometry and mathem…

We characterize the Lie derivative of spinor fields from a variational point of view by resorting to the theory of the Lie derivative of sections of gauge-natural bundles. Noether identities from the gauge-natural invariance of the first variational derivative of the Einstein(--Cartan)--Dirac Lagrangian provide restric…

We calculate the higher derivatives of length functions on Teichmuller space along earthquake deformations. This generalizes the cosine formula for the first derivative by Kerckhoff and Wolpert and the sine formula for second derivative by Wolpert.

Develops a new approach to study nonlinear PDEs and their singularities.

Derives derivatives of risk measures for various types of portfolio losses.

Optimizes material distribution on surfaces using topological derivatives.

Derives a formula for the k-th covariant derivative of tensor fields.

We present a unified derivation of covariant time derivatives, which transform as tensors under a time-dependent coordinate change. Such derivatives are essential for formulating physical laws in a frame-independent manner. Three specific derivatives are described: convective, corotational, and directional. The covaria…

Invariant covariant derivatives on homogeneous spaces are characterized.

Derives derivatives and geometric framework for functions with non-independent variables.

We explain how to translate several recent results in derived algebraic geometry to derived differential geometry. These concern shifted Poisson structures on NQ-manifolds, Lie groupoids, smooth stacks and derived generalisations, and include existence and classification of various deformation quantisations.

The problem of quantile hedging for basket derivatives in the Black-Scholes model with correlation is considered. Explicit formulas for the probability maximizing function and the cost reduction function are derived. Applicability of the results for the widely traded derivatives as digital, quantos, outperformance and …

In the spirit of Arrow-Debreu, we introduce a family of financial derivatives that act as primitive securities in that exotic derivatives can be approximated by their linear combinations. We call these financial derivatives signature payoffs. We show that signature payoffs can be used to nonparametrically price and hed…

Establishes equivalence between models of derived stacks.

New estimator for estimating derivatives in nonparametric regression.

We characterise the link of derivatives in measure, which are introduced in [AKR,Card,ORS] respectively by different means, for functions on the space $\mathbb M$ of finite measures over a Riemannian manifold $M$. For a reasonable class of functions $f$, the extrinsic derivative $D^Ef$ coincides with the linear functio…

Estimates cross-impact on derivatives markets using E-Mini futures and options.

Let $(M,g)$ be a pseudo-Riemannian manifold. We propose a new approach for defining the conformal Schwarzian derivatives. These derivatives are 1-cocycles on the group of diffeomorphisms of $M$ related to the modules of linear differential operators. As operators, these derivatives do not depend on the rescaling of the…