arXiv research

Proposes a new model to describe positive volatility-price correlation in commodity markets.

This paper is concerned with the asymptotics for Greeks of European-style options and the risk-neutral density function calculated under the constant elasticity of variance model. Formulae obtained help financial engineers to construct a perfect hedge with known behaviour and to price any options on financial assets.

This work extends elasticity theory to curved spaces, solving stress potentials.

The mixed-fractional CEV model improves CDS pricing by accounting for default risk.

New insights into stability of special curves on spheres.

This paper develops a European option pricing formula for fractional market models. Although there exist option pricing results for a fractional Black-Scholes model, they are established without accounting for stochastic volatility. In this paper, a fractional version of the Constant Elasticity of Variance (CEV) model …

This paper optimizes predicting support and resistance levels in financial markets.

We develop a theory of axisymmetric surfaces minimizing a combination of surface tension and nematic elastic energies which may be suitable for describing simple film and bubble shapes. As a function of the elastic constant and the applied tension on the bubbles, we find the analogues of the unduloid, sphere, and nodoi…

The energy minimization problem associated to uniform, isotropic, linearly elastic rods leads to a geometric variational problem for the rod centerline, whose solutions include closed, knotted curves. We give a complete description of the space of closed and quasiperiodic solutions. The quasiperiodic curves are paramet…

The theme in this paper is the recombining binomial tree to price American put option when the underlying stock follows constant elasticity of variance(CEV) process. Recombining nodes of binomial tree are decided from finite difference scheme to emulate CEV process and the tree has a linear complexity. Also it is deriv…

This study presents new analytic approximations of the stochastic-alpha-beta-rho (SABR) model. Unlike existing studies that focus on the equivalent Black-Scholes (BS) volatility, we instead derive the equivalent constant-elasticity-of-variance (CEV) volatility. Our approach effectively reduces the approximation error i…

Paper is based on "The cost of illiquidity and its effects on hedging", L. C. G. Rogers and Surbjeet Singh, 2010. We generalize its thesis to constant elasticity model, which own previously used Black-Schoels model as a special case. The Goal of this article is to find optimal hedging strategy of European call/put opti…

The Backlund transformation for pseudospherical surfaces, which is equivalent to that of the sine-Gordon equation, can be restricted to give a transformation on space curves that preserves constant torsion. We study its effects on closed curves (in particular, elastic rods) that generate multiphase solutions for the vo…

The paper proves rigidity for shells in non-Euclidean spaces.

Derives token price process for AMM tokens, finds leverage effect and pricing discrepancies.

The edge of torn elastic sheets and growing leaves often form a hierarchical buckling pattern. Within non-Euclidean plate theory this complex morphology can be understood as low bending energy isometric immersions of hyperbolic Riemannian metrics. With this motivation we study the isometric immersion problem in strip a…

Study of $p$-biharmonic curves and their properties.

We study a sparse negative binomial regression (NBR) for count data by showing the non-asymptotic advantages of using the elastic-net estimator. Two types of oracle inequalities are derived for the NBR's elastic-net estimates by using the Compatibility Factor Condition and the Stabil Condition. The second type of oracl…

Proposes HDBEN for heteroscedastic regression with improved sparsity and variance modeling.

Flow deforms locally convex curves to curves of constant k-order width.

Analyzes properties of stiffness tensors for elastic wave imaging.

I show that if the capital accumulation dynamics is stochastic a new term, in addition to that given by accounting prices, has to be introduced in order to derive a correct estimate of the genuine wealth of an economy. In a simple model with multiplicative accumulation dynamics I show that: 1) the value function is alw…

This paper introduces an elasticity reconstruction method based on local displacement observations of elastic bodies. Sparse reconstruction theory is applied to formulate the underdetermined inverse problems of elasticity reconstruction including unobserved areas. An online local clustering scheme called a superelement…

A well known result of Da Rios and Levi-Civita says that a closed planar curve is elastic if and only if it is stationary under the localized induction (or smoke ring) equation, where stationary means that the evolution under the localized induction equation is by rigid motions. We prove an analogous result for surface…

Elastic Cash adjusts money supply to stabilize interest rates.

Characterizes null Lagrangians in Cosserat elasticity.

Approximate 3D elastic curves with exact constraints

The paper studies rigidity and continuity in nonlinear elasticity on manifolds and hypersurfaces.

Study preserves planar and graphical properties of curves under elastic flow.

The paper studies the free elastic flow of closed curves and finds their asymptotic shape converges to a circle.

Motivated by the problem of finding an explicit description of a developable narrow Moebius strip of minimal bending energy, which was first formulated by M. Sadowsky in 1930, we will develop the theory of elastic strips. Recently E.L. Starostin and G.H.M. van der Heijden found a numerical description for an elastic Mo…

Study on migrating elastic flows of curves across half-planes.

Study gauge freedoms in elastic wave equations and Dirichlet-to-Neumann map.

Solves curve migration problem with elastic flows.

Due to the advantage of achieving a better performance under weak regularization, elastic net has attracted wide attention in statistics, machine learning, bioinformatics, and other fields. In particular, a variation of the elastic net, adaptive elastic net (AEN), integrates the adaptive grouping effect. In this paper,…

Symmetric elastic knots are found for certain classes with dihedral symmetry.

We study a class of elastic energy functionals for maps between planar domains (among them the so-called squared distance functional) whose critical points (elastic maps) allow a far more complete theory than one would expect from general elasticity theory. For some of these functionals elastic maps even admit a "Weier…

Study of elastic models in non-Euclidean spaces via Γ-convergence.

New discrete curves defined in space forms with geometric properties.

Demand variance can result in a mismatch between planned supply and actual demand. Demand shaping strategies such as pricing can be used to shift elastic demand to reduce the imbalance. In this work, we propose to consider elastic demand in the forecasting phase. We present a method to reallocate the historical elastic…

We present a rigorous study of the short maturity asymptotics for Asian options with continuous-time averaging, under the assumption that the underlying asset follows the Constant Elasticity of Variance (CEV) model. We present an analytical approximation for the Asian options prices which has the appropriate short matu…

The elastic flow, which is the $L^2$-gradient flow of the elastic energy, has several applications in geometry and elasticity theory. We present stable discretizations for the elastic flow in two-dimensional Riemannian manifolds that are conformally flat, i.e.\ conformally equivalent to the Euclidean space. Examples in…

Unified survey of elastic flow for curves and networks.

Study on elastic curves with variable stiffness, derived from bending energy.

Study on closed $p$-elastic curves in hyperbolic and de Sitter planes.

Biharmonic curves are a generalization of geodesics, with applications in elasticity theory and various branches of computer science. The paper proposes a first study of biharmonic curves in spaces with Finslerian geometry, covering the following topics: a deduction of their equations, existence of non-geodesic biharmo…

In non-linear incompatible elasticity, the configurations are maps from a non-Euclidean body manifold into the ambient Euclidean space, $\mathbb{R}^k$. We prove the $Γ$-convergence of elastic energies for configurations of a converging sequence, $\mathcal{M}_n\to\mathcal{M}$, of body manifolds. This convergence result …

Study on Transfer Elastic Net error bounds and grouping effect.