Consider a non-spanned security CT in an incomplete market. We study the risk/return tradeoffs generated if this security is sold for an arbitrage-free price b C0 and then hedged. We consider recursive “one-period optimal” self-financing hedging strategies, a simple but tractable criterion. For continuous trading, diffusion processes, the one-period minimum variance portfolio is optimal. Let C0...

A Banach space E is c0-saturated if every closed infinite dimensional subspace of E contains an isomorph of c0. A c0-saturated Banach space with an unconditional basis which has a quotient space isomorphic to l2 is constructed. A Banach space E is c0-saturated if every closed infinite dimensional subspace of E contains an isomorph of c0. In [2] and [3], it was asked whether all quotient spaces ...

This note gives a simplified proof of the similarity between the Mandelbrot set and the quadratic Julia sets at the Misiurewicz parameters, originally due to Tan Lei [TL]. We also give an alternative proof of the global linearization theorem of repelling fixed points. 1 Simlarity between M and J We first give a proof of Tan’s theorem, in a way inspired by Schwick [Sch]. The Julia sets and the M...

We show that the class of subspaces of c0(N) is stable under Lipschitz isomorphisms. The main corollary is that any Banach space which is Lipschitz-isomorphic to c0(N) is linearly isomorphic to c0(N). The proof relies in part on an isomorphic characterization of subspaces of c0(N) as separable spaces having an equivalent norm such that the weak-star and norm topologies quantitatively agree on t...

We give an explicit extension of Spencer’s result on the biplanar crossing number of the ErdősRényi random graph G(n, p). In particular, we show that the k-planar crossing number of G(n, p) is almost surely Ω((np)). Along the same lines, we prove that for any fixed k, the k-planar crossing number of various models of random d-regular graphs is Ω((dn)) for d > c0 for some constant c0 = c0(k).

We characterize generators of polynomially bounded C0-semigroups in terms of an integrability condition for the second power of the resolvent on vertical lines. This generalizes results by Gomilko, Shi and Feng on bounded semigroups and by Malejki on polynomially bounded groups.

The GHS attack is known to solve discrete logarithm problems (DLP) in the Jacobian of a curve C0 defined over the d degree extension field kd of k := Fq by mapping it to the DLP in the Jacobian of a covering curve C of C0 over k. Recently, classifications for all elliptic curves and hyperelliptic curves C0/kd of genus 2,3 which possess (2, ..., 2)-covering C/k of P were shown under an isogeny c...

In this retrospective study, cyclosporine levels at the second hour (C2 levels) were measured during oral cyclosporine intake in 28 pediatric hematopoietic stem cell transplant patients, and the relations between cyclosporine dosage and C0, C2 levels, C2/C0 ratio, and cyclosporine-related adverse effects were investigated. Cyclosporine levels at the second hour levels were found to be significa...