Local forms of molecular mobility in copolymethacrylates containing side‐chain nonlinear optical chromophores

Local forms of molecular mobility of comb‐like random copolymethacrylates, containing side‐chain nonlinear optical chromophores and amyl‐ or octafluoroamyl‐groups, are studied. In the glassy state, two relaxation processes are found, which are due to reorientation of terminal polar groups (γ₂‐process) and rotation of chromophore groups about their long axes (β‐process). For octafluoroamyl‐containing copolymers, the γ₂‐process is superposition of the two molecular motions due to reorientation of terminal chromophore groups and ? CF₂H groups. The intensity and relaxation times in the range of the γ₂‐process depend on the chemical structure and concentration of chromophores in a copolymer. For the β‐process, the molecular mobility weakly depends on the chromophore structure, being mainly determined by the relative lengths of the rigid chromophore and flexible side chains. On the global spectrum of depolarization current it was observed the γ₁‐process due to reorientation of (CH₂)_n spacers between chromophore groups and copolymer backbone. © 2008 Wiley Periodicals, Inc. J Polym Sci Part B: Polym Phys 46: 1488–1496, 2008     

Extreme value distribution of a recursive-type detector in a linear model

We study a CUSUM–type monitoring scheme designed to sequentially detect changes in the regression parameter of an underlying linear model. The test statistic used is based on recursive residuals. Main aim of this paper is to derive the limiting extreme value distribution under the null hypothesis of structural stability. The model assumptions are flexible enough to include rather general classes of error sequences such as augmented GARCH(1,1) processes. The result is underlined by an illustrative simulation study. Research partially supported by NSF grants DMS–0604670 and DMS–065242.     

Prices and sensitivities of Asian options: A survey

Asian options are hard to price both analytically and numerically. Even though they have been the focus of much attention in recent years, there is no single technique which is widely accepted to price Asian options for all choices of market parameters. For hedging purposes, the estimation of the price sensitivities is often as important as the evaluation of the prices themselves. This paper provides a survey of current methods for pricing Asian options and computing their sensitivities to the key input parameters. The methods discussed include: Monte Carlo simulation, the finite difference approach and various quasi analytical approaches and approximations. We discuss practical numerical issues that arise in implementing these methods. The paper compares the accuracy and efficiency of the different approaches and offers some general conclusions.     

Set Partition Complexes

The Hom complexes were introduced by Lovász to study topological obstructions to graph colorings. The vertices of Hom(G,K _n ) are the n-colorings of the graph G, and a graph coloring is a partition of the vertex set into independent sets. Replacing the independence condition with any hereditary condition defines a set partition complex. We show how coloring questions arising from, for example, Ramsey theory can be formulated with set partition complexes. It was conjectured by Babson and Kozlov, and proved by Čukić and Kozlov, that Hom(G,K _n ) is (n−d−2)-connected, where d is the maximal degree of a vertex of G. We generalize this to set partition complexes.     

Calibration of the default probability model

In this paper, we study the calibration problem for the Merton–Vasicek default probability model [Robert Merton, On the pricing of corporate debt: the risk structure of interest rate, Journal of Finance 29 (1974) 449–470]. We derive conditions that guarantee existence and uniqueness of the solution. Using analytical properties of the model, we propose a fast calibration procedure for the conditional default probability model in the integrated market and credit risk framework. Our solution allows one to avoid numerical integration problems as well as problems related to the numerical solution of the nonlinear equations.     

Principal eigenvalues and the Dirichlet problem for fully nonlinear elliptic operators

We study uniformly elliptic fully nonlinear equations of the type F(D²u,Du,u,x)=f(x). We show that convex positively 1-homogeneous operators possess two principal eigenvalues and eigenfunctions, and study these objects; we obtain existence and uniqueness results for nonproper operators whose principal eigenvalues (in some cases, only one of them) are positive; finally, we obtain an existence result for nonproper Isaac's equations.