Optimal closing of a pair trade with a model containing jumps

A pair trade is a portfolio consisting of a long position in one asset and a short position in another, and it is a widely used investment strategy in the financial industry. Recently, Ekström, Lindberg, and Tysk studied the problem of optimally closing a pair trading strategy when the difference of the two assets is modelled by an Ornstein-Uhlenbeck process. In the present work the model is generalized to also include jumps. More precisely, we assume that the difference between the assets is an Ornstein-Uhlenbeck type process, driven by a Lévy process of finite activity. We prove a necessary condition for optimality (a so-called verification theorem), which takes the form of a free boundary problem for an integro-differential equation. We analyze a finite element method for this problem and prove rigorous error estimates, which are used to draw conclusions from numerical simulations. In particular, we present strong evidence for the existence and uniqueness of an optimal solution.     

Separation of arsenic from germanium oxide targets by dry distillation

Positron-emitting isotopes of arsenic, ⁷⁰As (T _1/2 = 53 min), ⁷¹As (T _1/2 = 64 h), ⁷²As (T _1/2 = 26 h), and ⁷³As (T _1/2 = 17.8 d) are of interest in biomedical investigations using PET. A fast and simple method for their production using low-energy proton and deuteron reactions on enriched Ge-targets is presented. Dry distillation of GeO₂ at 1105 °C during 2 hours provides a separation efficiency of more than 60%. The loss of target material is less than one per cent and the irradiated targets can be used several times. The method allows production of diagnostically useful amounts of positron-emitting arsenic isotopes using accelerators commonly available at PET-centres.     

Interpolation of coefficients and transformation of the dependent variable in finite element methods for the non-linear heat equation

Error estimates are shown for some spatially discrete Galerkin finite element methods for a non-linear heat equation. The approximation schemes studied are based on the introduction of the enthalpy as a new dependent variable, and also on the application of the Kirchhoff transformation and on interpolation of the non-linear coefficients into standard Lagrangian finite element spaces.     

Experimental investigation of ice slurry flow pressure drop in horizontal tubes

Pressure drop behaviour of ice slurry based on ethanol–water mixture in circular horizontal tubes has been experimentally investigated. The secondary fluid was prepared by mixing ethyl alcohol and water to obtain initial alcohol concentration of 10.3% (initial freezing temperature ?4.4 °C). The pressure drop tests were conducted to cover laminar and slightly turbulent flow with ice mass fraction varying from 0% to 30% depending on test conditions. Results from flow tests reveal much higher pressure drop for higher ice concentrations and higher velocities in comparison to the single phase flow. However for ice concentrations of 15% and higher, certain velocity exists at which ice slurry pressure drop is same or even lower than for single phase flow. It seems that higher ice concentration delay flow pattern transition moment (from laminar to turbulent) toward higher velocities. In addition experimental results for pressure drop were compared to the analytical results, based on Poiseulle and Buckingham–Reiner models for laminar flow, Blasius, Darby and Melson, Dodge and Metzner, Steffe and Tomita for turbulent region and general correlation of Kitanovski which is valid for both flow regimes. For laminar flow and low buoyancy numbers Buckingham–Reiner method gives good agreement with experimental results while for turbulent flow best fit is provided with Dodge–Metzner and Tomita methods.Furthermore, for transport purposes it has been shown that ice mass fraction of 20% offers best ratio of ice slurry transport capability and required pumping power.     

VAPOR PRESSURES OF FRAGRANCE COMPOUNDS DURING CONTROLLED EVAPORATION

The content of each of the three components in the vapor phase from a phenethyl alcohol, - limonene - decane solution was determined from the composition of the condensed phase during controlled evaporation with turbulent gas flow, with complete removal of the vapor phase once per second and the values compared to those from vapor pressures determined at equilibrium.

The results showed the vapor composition during rapid removal of the vapor to be surprisingly similar to the equilibrium values.     

Ueber die Bindung des Jods an Stärke. I

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