We study a convex regularization of the local volatility surface identification problem for the Black-Scholes partial differential equation from prices of European call options. This is a highly nonlinear ill-posed problem which in practice is subject to different noise levels associated to bid-ask spreads and sampling errors. We analyze, in appropriate function spaces, different properties of ...

The property of synergy and its detection are discussed. A response surface is said to possess synergy if it is monotone in each argument and its level curves are convex. Detecting this property is particularly useful in the study of combination drug therapies where the goal is enhanced response or diminished side effect. One way to detect synergy is to fit a surface with linear level curves un...

in this paper we introduce the concept of topological number for locally convex topological spaces and prove some of its properties. it gives some criterions to study locally convex topological spaces in a discrete approach.

Let S be a closed oriented surface of genus at least two. Labourie and the author have independently used the theory of hyperbolic affine spheres to find a natural correspondence between convex RP structures on S and pairs (Σ, U) consisting of a conformal structure Σ on S and a holomorphic cubic differential U over Σ. The pairs (Σ, U), for Σ varying in moduli space, allow us to define natural h...

The convex–concave rule is considered an important theory during treatment decision-making (Kirby et al., 2007). According to this rule (Fig. 1) the therapist moves a bone with a convex joint surface opposite to the direction of restricted movement of the distal aspect of the bone (e.g. the head of humerus inferiorly for restricted shoulder abduction). However, a concave joint surface is mobili...

Cooper and Long generalised Epstein and Penner’s Euclidean cell decomposition of cusped hyperbolic n–manifolds of finite volume to non-compact strictly convex projective n–manifolds of finite volume. We show that Weeks’ algorithm to compute this decomposition for a hyperbolic surface generalises to strictly convex projective surfaces.

We characterize convex cocompact subgroups of the mapping class group of a surface in terms of uniform convergence actions on the zero locus of the limit set. We also construct subgroups that act as uniform convergence groups on their limit sets, but are not convex cocompact.

This paper provides four alternative suucient condition-sets, ensuring that a patch of a parametric tensor-product B-spline surface is locally convex. These conditions are at most tri-quadratic with respect to the control points of the surface.

In this paper, firstly, we obtain some new results about bornological convergence in locally convex cones (which was studied in [1]) and then we introduce the concept of bornological completion for locally convex cones. Also, we prove that the completion of a bornological locally convex cone is bornological. We illustrate the main result by an example.