On the Price of Risk of the Underlying Markov Chain in a Regime-Switching Exponential Lévy Model

Regime-switching models (RSM) have been recently used in the literature as alternatives to the Black-Scholes model. Several authors favor RSM as being more realistic since, by construction, they model those exogenous macroeconomic cycles against which asset prices evolve. In the context of derivatives pricing, these models lead to incomplete markets and therefore there exist multiple Equivalent Martingale Measures (EMM) yielding different pricing rules. A fair amount of literature (Buffington and Elliott, Int J Theor Appl Finance 40:267–282, 2002; Elliott et al., Ann Finance 1(4):23–432, 2005) focuses on conveniently choosing a family of EMM leading to closed-form formulas for option prices. These studies often make the assumption that the risk associated with the Markov chain is not priced. Recently, Siu and Yang (Acta Math Appl Sin Engl Ser 25(3):339–388, 2009), proposed an EMM kernel that takes into account all risk components of a regime-switching Black-Scholes model. In this paper, we extend the results and observations made in Siu and Yang (Acta Math Appl Sin Engl Ser 25(3):339–388, 2009) in order to include more general Lévy regime-switching models that allow us to assess the influence of jumps on the price of risk. In particular, numerical results are given for Regime-switching Jump-Diffusion and Variance-Gamma models. Also, we carry out a comparative analysis of the resulting option price formulas with existing regime-switching models such as Naik (J Financ 48:1969–1984, 1993) and Boyle and Draviam (Insur Math Econ 40:267–282, 2007).     

Five loop Konishi from AdS/CFT

We derive the perturbative five loop anomalous dimension of the Konishi operator in N=4$N=4$ SYM theory from the integrable string sigma model by evaluating finite size effects using Lüscher formulas adapted to multimagnon states at weak coupling. In addition, we derive the five loop wrapping contribution for the L=2$L=2$ single impurity state in the β deformed theory, which may be within reach of a direct perturbative computation. The Konishi expression exhibits two new features — a modification of Asymptotic Bethe Ansatz quantization and sensitiveness to an infinite set of coefficients of the BES/BHL dressing phase. The result satisfies nontrivial self-consistency conditions — simple transcendentality structure and cancellation of μ-term poles. It may be a testing ground for the proposed AdS/CFT TBA systems.     

A Strategy Utilizing a Recyclable Macrocycle Transporter for the Efficient Synthesis of a Triazolium‐Based [2]Rotaxane

A general synthesis of triazolium‐containing [2]rotaxanes, which could not be accessed by other methods, is reported. It is based on a sequential strategy starting from a well‐designed macrocycle transporter which contains a template for dibenzo‐24‐crown‐8 and a N‐hydroxysuccinimide (NHS) moiety. The sequence is: 1) synthesis by slippage of a [2]rotaxane building‐block; 2) its elongation at its NHS end; 3) the delivery of the macrocycle to the elongated part of the axle by an induced translational motion; 4) the contraction process to yield the targeted [2]rotaxane and recycle the initial transporter.     

Numerical modelling of optical trapping in hollow photonic crystal cavities

Photonic crystal (PhC) devices owing to their strong confinement of electromagnetic energy are considered to be excellent candidates for on chip optical trapping of dielectric or biological particles in the nanometer range. In this work, we study and present hollow PhC cavities and characterize them for their trapping stiffness, trapping stability and variation of resonance wavelength due to the presence of various sized single particles in the cavity.     

Rare-earth metal alkyl and hydride complexes stabilized by a cyclen-derived [NNNN] macrocyclic ancillary ligand

A trinuclear rare-earth metal hydride complex was synthesized from the dialkyl complex supported by a monoanionic [NNNN] macrocycle and shown to catalyze the hydrosilylation of olefins efficiently.     

All-cis cyclic peptides

Amide bonds -NH-CO- preferentially exist in trans conformations, the cis conformation being thermodynamically unfavored with respect to the trans by about 2 kcal/mol. Yet, the main reason most proteins or peptides cannot be made from cis-peptide plaques only lies in that connecting them into open chains appears to be sterically impracticable. It is possible, however, to build all-cis cyclic peptides in which all cis-plaques are efficiently locked. The present work examines, through quantum calculations, the structural and energetic issues associated with these peculiar arrangements. Systematic exploration at DFT-B3LYP level of the potential-energy surfaces for all-cis cyclopolyglycines cG(n)(c) (n = 2-10,15), and to a lesser extent, for all-cis cyclopolyalanines and all-cis cyclopolyphenylalanines confirms that all these structures are true minima. Optimal ring size occurs around eight peptide units, resulting in planar cG7(c), cG8(c), and cG9(c). In smaller systems, the ring strain is relieved through nonplanar cup-like distortions, particularly in cG6(c). From 10 peptide units and beyond, the ring framework distorts into a saddle-edge shape. These molecules disclose some molecular flexibility, as combinatorial tilting of the plaques may give sets of minima close in energy. Indexes based on isodesmic reactions are used to estimate the energy for joining all-cis or all-trans plaques into cyclic peptides. One of them, the mean plaque-junction energy (MPJE) suggests that within sensible sizes from six peptide units and beyond, all-cis plaque association is almost equally favorable as all-trans one. The frame of radiating cis-amide bonds can be considered as defining a new kind of peptidic material, endowed with specific self-assembling properties.     

High extraction efficiency,laterally injected,light emitting diodes combining microcavities and photonic crystals

The use of photonic crystals (PCs) for realistic light emitting diodes (LEDs) is discussed, given the constraints of planar semiconductor technology. A viable route for the fabrication of high-efficiency high-brightness electrically injected LEDs is presented. The starting point is a top-emitting microcavity using a single Alox Bragg mirror. The active area is surrounded by two-dimensional PCs, namely arrays of air rods etched through the top layers; injection of the electrons is achieved through the crystals. Design rules for PCs as efficient out-couplers are detailed. The building blocks are assessed experimentally, and we show that promising results are at hand.     

Mechanical, rheological, fatigue, and degradation behavior of PLLA, PGLA and PDGLA as materials for vascular implants

The biggest challenge in the treatment of arterial stenosis remains the issue of optimization of stent design. Despite continuous improvement in surgical techniques and use of intensive pharmacotherapy, the results of stent coronary interventions may be unsatisfactory, and long-term interaction of a metal implant with a blood vessel results in complications such as recurrent stenosis and thrombosis. Therefore, it is necessary to search for new materials and stent designs to obtain a stent capable of restoring flow in the vessel and disappearing after fulfilling its function. Such stent must also be compatible with the vessel wall to enable regeneration of new structure of endothelium and deeper artery layers damaged during implantation. Consequently, there is ongoing search for functional solutions with minimum effects of long-term implant-tissue interaction. In light of the above, the team investigated the possibility of using biodegradable polymers already mentioned in the literature as a construction material for vascular stent. The study used three polyhydroxyacids based on lactic acid and glycolic acid: poly(l-lactide), poly(lactide-co-glycolide) and poly(d,l-lactide-co-glycolide). The research focused on assessing changes in mechanical, thermomechanical, rheological, and fatigue properties during the process of hydrolytic degradation. The analysis also covered the rate of release of degradation products. The results of the conducted tests indicate the possibility of developing a vascular stent with biodegradable polymers.