Optimal Exercise Strategies for Operational Risk Insurance via Multiple Stopping Times

In this paper we demonstrate how to develop analytic closed form solutions to optimal multiple stopping time problems arising in the setting in which the value function acts on a compound process that is modified by the actions taken at the stopping times. This class of problem is particularly relevant in insurance and risk management settings and we demonstrate this on an important application domain based on insurance strategies in Operational Risk management for financial institutions. In this area of risk management the most prevalent class of loss process models is the Loss Distribution Approach (LDA) framework which involves modelling annual losses via a compound process. Given an LDA model framework, we consider Operational Risk insurance products that mitigate the risk for such loss processes and may reduce capital requirements. In particular, we consider insurance products that grant the policy holder the right to insure k of its annual Operational losses in a horizon of T years. We consider two insurance product structures and two general model settings, the first are families of relevant LDA loss models that we can obtain closed form optimal stopping rules for under each generic insurance mitigation structure and then secondly classes of LDA models for which we can develop closed form approximations of the optimal stopping rules. In particular, for losses following a compound Poisson process with jump size given by an Inverse-Gaussian distribution and two generic types of insurance mitigation, we are able to derive analytic expressions for the loss process modified by the insurance application, as well as closed form solutions for the optimal multiple stopping rules in discrete time (annually). When the combination of insurance mitigation and jump size distribution does not lead to tractable stopping rules we develop a principled class of closed form approximations to the optimal decision rule. These approximations are developed based on a class of orthogonal Askey polynomial series basis expansion representations of the annual loss compound process distribution and functions of this annual loss.     

An upper bound on the Chebotarev invariant of a finite group

A subset {g ₁,..., g _d } of a finite group G invariably generates \(\left\{ {g_1^{{x_1}}, \ldots ,g_d^{{x_d}}} \right\}\) generates G for every choice of x _i ∈ G. The Chebotarev invariant C(G) of G is the expected value of the random variable n that is minimal subject to the requirement that n randomly chosen elements of G invariably generate G. The first author recently showed that \(C\left( G \right) \leqslant \beta \sqrt {\left| G \right|} \) for some absolute constant β. In this paper we show that, when G is soluble, then β is at most 5/3. We also show that this is best possible. Furthermore, we show that, in general, for each ε > 0 there exists a constant c _ε such that \(C\left( G \right) \leqslant \left( {1 + \in } \right)\sqrt {\left| G \right|} + {c_ \in }\).     

The Structure of Uniform Discrete Defective Crystals

In the continuum context, a uniform crystal has dislocation density tensor constant in space. A simple iteration procedure generates an infinite set of points which is associated with uniform defective crystals. When certain necessary conditions are satisfied, there is a minimum (non-zero) separation of points in this set, so the set is discrete. We describe the structure of such sets explicitly, and show in particular that any such set is either a simple lattice or a 4-lattice.Paolo Cermelli was partially supported by the Italian MIUR grant ‘Modelli Matematici per la Scienza dei Materiali’.     

Fabrication of spiropyran-containing thin film sensors used for the simultaneous identification of multiple metal ions

In this article, a methacrylate-based spiropyran-containing copolymer was used as a colorimetric sensor to identify multiple metal ions simultaneously. Through UV-vis absorption spectroscopy, the relative binding affinity of merocyanine to each metal ion was investigated by displacement studies of a bound metal ion with a second metal ion of a higher binding affinity. We also show that because each metal ion gives rise to a distinct spectral response, partial least-squares discriminant analysis (PLS-DA) can be used to analyze the UV-vis absorbance spectra to identify the two metal ions that are present in solution at varying concentrations simply by dipping a coated polymer substrate into solution after irradiation. Partial least-squares regression analysis (PLS) was used to determine the metal ions in solution for several binary mixtures quantitatively. We also demonstrate that the quantitative determination depends on the relative binding preference of merocyanine to each metal ion.     

Surface-confined nickel mediated cross-coupling reactions: characterization of initiator environment in Kumada catalyst-transfer polycondensation

Kumada catalyst-transfer polycondensation (KCTP) has proven to be an excellent strategy toward the synthesis of well-defined conjugated polymers. In this report, Ni(0) species are reacted with surface-bound aryl bromides to yield KCTP initiators of structure (aryl)Ni(II)-Br. Surface-confined Kumada reactions are carried out with a ferrocene functionalized Grignard reagent to quantify initiator coverage, ligand exchange, and Kumada reaction kinetics. In addition, surface-initiated Kumada catalyst-transfer polycondensation (SI-KCTP) is carried out from the fabricated initiators to modify SiO(2) and ITO surfaces. Uniform poly(3-methylthiophene) films with thicknesses between 40 and 65 nm were characterized using a variety of spectroscopic and electrochemical techniques.     

N,N'-Carbonyldiimidazole-mediated functionalization of superparamagnetic nanoparticles as vaccine carrier

Particulates with specific sizes and characteristics can induce potent immune responses by promoting antigen uptake of appropriate immuno-stimulatory cell types. Magnetite (Fe(3)O(4)) nanoparticles have shown many potential bioapplications due to their biocompatibility and special characteristics. Here, superparamagnetic Fe(3)O(4) nanoparticles (SPIONs) with high magnetization value (70emug(-1)) were stabilized with trisodium citrate and successfully conjugated with a model antigen (ovalbumin, OVA) via N,N'-carbonyldiimidazole (CDI) mediated reaction, to achieve a maximum conjugation capacity at approximately 13 microgmicrom(-2). It was shown that different mechanisms governed the interactions between the OVA molecules and magnetite nanoparticles at different pH conditions. We evaluated as-synthesized SPION against commercially available magnetite nanoparticles. The cytotoxicity of these nanoparticles was investigated using mammalian cells. The reported CDI-mediated reaction can be considered as a potential approach in conjugating biomolecules onto magnetite or other biodegradable nanoparticles for vaccine delivery.     

Measuring screw-sense preference in a helical oligomer by comparison of 13C NMR signal separation at slow and fast exchange

While an unequal population of rapidly interconverting left- and right-handed conformers of a helical oligomer can be detected by circular dichroism, precise quantification of a conformer ratio has not previously been achieved. We demonstrate, using a set of labeled peptide analogues, that simple analysis of peak separation in their (13)C NMR spectra at slow and fast exchange allows an accurate value for the ratio of helical conformers to be obtained. The method reports the ratio of conformers at the site of the label and can therefore be used to investigate local variations in helical conformational control.     

Inorganic approaches for radiolabelling biomolecules with fluorine-18 for imaging with positron emission tomography

Conventional methods for radiolabelling biomolecules such as proteins and peptides with fluorine-18 for PET imaging rely on carbon-fluorine bond formation and are complex and inefficient. Several non-carbon elements form strong bonds (i.e. with high bond enthalpy) with fluorine, but with lower activation energy for their formation compared to carbon-fluorine bonds, whilst preserving a relatively high kinetic stability. In particular, by incorporating boron-, aluminium- and silicon-containing prosthetic groups into biomolecules, promising results have recently been achieved in the radiolabelling with F-18-fluoride under mild aqueous conditions, affording a level of convenience, efficiency and specific activity potentially superior to those offered by conventional C-F bond formation methods. The promise already shown by these early studies heralds a new branch of bioconjugate radiochemistry involving a wider range of "fluoridephilic" elements for synthesis of PET molecular imaging agents.     

New insights into the intercalation chemistry of Al(OH)3

This paper reports a number of recent developments in the intercalation chemistry of Al(OH)(3). From Rietveld refinement and solid-state NMR, it has been possible to develop a structural model for the recently reported [M(II)Al(4)(OH)(12)](NO(3))(2)·yH(2)O family of layered double hydroxides (LDHs). The M(2+) cations occupy half of the octahedral holes in the Al(OH)(3) layers, and it is thought that there is complete ordering of the metal ions while the interlayer nitrate anions are highly disordered. Filling the remainder of the octahedral holes in the layers proved impossible. While the intercalation of Li salts into Al(OH)(3) is facile, it was found that the intercalation of M(II) salts is much more capricious. Only with Co, Ni, Cu, and Zn nitrates and Zn sulfate were phase-pure LDHs produced. In other cases, there is either no reaction or a phase believed to be an LDH forms concomitantly with impurity phases. Reacting Al(OH)(3) with mixtures of M(II) salts can lead to the production of three-metal M(II)-M(II)'-Al LDHs, but it is necessary to control precisely the starting ratios of the two M(II) salts in the reaction gel because Al(OH)(3) displays selective intercalation of M nitrate (Li > Ni > Co ≈ Zn). The three-metal M(II)-M(II)'-Al LDHs exhibit facile ion exchange intercalation, which has been investigated in the first energy dispersive X-ray diffraction study of a chemical reaction system performed on Beamline I12 of the Diamond Light Source.