Unifying pricing formula for several stochastic volatility models with jumps

In this paper, we introduce a unifying approach to option pricing under continuous‐time stochastic volatility models with jumps. For European style options, a new semi‐closed pricing formula is derived using the generalized complex Fourier transform of the corresponding partial integro‐differential equation. This approach is successfully applied to models with different volatility diffusion and jump processes. We also discuss how to price options with different payoff functions in a similar way. In particular, we focus on a log‐normal and a log‐uniform jump diffusion stochastic volatility model, originally introduced by Bates and Yan and Hanson, respectively. The comparison of existing and newly proposed option pricing formulas with respect to time efficiency and precision is discussed. We also derive a representation of an option price under a new approximative fractional jump diffusion model that differs from the aforementioned models, especially for the out‐of‐the money contracts. Copyright © 2017 John Wiley & Sons, Ltd.     

Zur Schurgruppe eines lokalen Körpers

Ohne Zusammenfassung     

On the Arf invariant in historical perspective, part?2

This is a continuation of our previous article (Lorenz and Roquette in Math. Semesterber. 57(1):73?C102, 2010) in this journal, where we discussed the paper of Cahit Arf (J. Reine Angew. Math. 183:148?C167, 1941). There he introduced what today is called the ??Arf invariant?? of a quadratic form over a field of characteristic?2. After our article had appeared we obtained some new information about the present state of the theory. When we say ??new?? then this means that this was new to us, i.e., we had not been aware before of the literature on the subject. (See our list of references.) It seems worthwhile to us to report here about it, as far as it is relevant for the assessment of Arf??s paper in its historical perspective.     

Kinetics of dark excitons and excitonic trions in InGaAs single quantum well

Magnetooptical studies performed on a wide InGaAs/GaAs single quantum well indicate that optically non-active (dark) excitons with total angular momentum play the role of a reservoir for the creation of free multiparticle excitonic complexes. After analyzing the magnetic field evolution of the circularly polarized components of the low energy structure appearing in the main excitonic luminescence line we assign this feature to the excitonic trion formation. The binding energy of the excitonic trions was estimated to be of the order of 1 meV. Received: 29 October 1997 / Received in final form: 20 February 1998 / Accepted: 21 February 1998     

Charaktere endlicher Gruppen mit vorgegebenen Schurschen Indizes

Ohne Zusammenfassung     

Nanocellulose Polymer Composites as Innovative Pool for (Bio)Material Development

Summary: Using a “never-dried” procedure (according to Figure 4) shaped bacterial nanocellulose (BC, 1% cellulose, 99% water) has been modified by the formation of BC-polymer composites. For this purpose, acrylate and methacrylate monomers and methacrylate crosslinkers were photopolymerized inside an ethanol-swollen nanofiber network. Using the ethanol as solvent and as confirmed by model reactions the synthetic polymer (SP) part of the composites is constructed of crosslinked polymers (number of repeating units in the range of 500). As part of ongoing work on the development of (bio)materials from the innovative pool of BC composites these investigations are recently directed towards the creation of collagen-like materials. Thus, for these purposes, mainly water absorption capacity, strength, and elasticity have to be controlled, whilst still retaining essential features of BC like shape, nanofiber network, pore system, and proved biocompatibility. Using acrylic acid, 2-ethylhexyl acrylate, 2-hydroxyethyl methacrylate, N-vinyl pyrrolidone as acrylate monomers and triethylene glycol dimethacrylate and 1,4-butandiol dimethacrylate as crosslinkers of different concentrations either a filling of the pores or a coating of the fibers in the BC nanocomposites could be achieved. The small cellulose content of the composites significantly increases the water absorption value and the strength of the material as well as the ability of re-swelling in the case of fiber coated composites. Sample 12 is an optimized BC-SP composite regarding important properties of hyaline cartilage like Young's modulus in the range of 5–20 MPa using the well-known Simplex-method.     

Remobilization of pentavalent antimony and vanadium from a granular iron hydroxide material--a comparative study of different leaching systems

The remobilization of antimony and vanadium from previously loaded commercial granular ferric-hydroxide GEH material (intended for water treatment) was examined by using a sequential extraction procedure and three different leaching systems to evaluate their physicochemical mobility and potential availability under different simulated environmental conditions. A classical batch extraction, an extraction cell (EC) and rotating-coiled columns (RCC) were used as extraction systems.For each system it could be shown that the content of ion-exchangeable antimony and vanadium in previously loaded material is negligible (<1.5%). The oxyanions were sorbed strongly and could be predominantly remobilized through reducing agents, which means through dissolution of the iron (hydr)oxide matrix.The major advantages of dynamic systems in comparison to batchwise fractionation technique are the drastically reduced extraction time and the possibility of generating information to the leaching kinetics. It is shown that the efficiency of the three leaching systems is quite different employing Wenzel's sequential fractionation protocol. Only by working with RCC, the iron (hydr)oxide matrix was completely dissolved within four steps resulting in the total mobilization of antimony and vanadium. EC seems to be less suitable for leaching studies of Sb and V sorbed on iron(hydr)oxide. The remobilizable proportion of the several fractions was lower in comparison to batch and RCC and seems to be a result of an agglomeration of the GEH in the EC device.