Admissible strategies in semimartingale portfolio selection

The choice of admissible trading strategies in mathematical modelling of financial markets is a delicate issue, going back to Harrison and Kreps [HK79]. In the context of optimal portfolio selection with expected utility preferences this question has been the focus of considerable attention over the last twenty years. We propose a novel notion of admissibility that has many pleasant features { admissibility is characterized purely under the objective measure P; each admissible strategy can be approximated by simple strategies using finite number of trading dates; the wealth of any admissible strategy is a supermartingale under all pricing measures; local boundedness of the price process is not required; neither strict monotonicity, strict concavity nor differentiability of the utility function are necessary; the definition encompasses both the classical mean-variance preferences and the monotone expected utility. For utility functions finite on R, our class represents a minimal set containing simple strategies which also contains the optimizer, under conditions that are milder than the celebrated reasonable asymptotic elasticity condition on the utility function

Finitely generated ideal languages and synchronizing automata

We study representations of ideal languages by means of strongly connected synchronizing automata. For every finitely generated ideal language L we construct such an automaton with at most 2^n states, where n is the maximal length of words in L. Our constructions are based on the De Bruijn graph.Comment: Submitted to WORDS 201

Effect of pressure cycling on Iron: Signatures of an electronic instability and unconventional superconductivity

High pressure electrical resistivity and x-ray diffraction experiments have been performed on Fe single crystals. The crystallographic investigation provides direct evidence that in the martensitic $bcc \rightarrow hcp$ transition at 14 GPa the $\lbrace 110\rbrace_{bcc}$ become the $\lbrace 002\rbrace_{hcp}$ directions. During a pressure cycle, resistivity shows a broad hysteresis of 6.5 GPa, whereas superconductivity, observed between 13 and 31 GPa, remains unaffected. Upon increasing pressure an electronic instability, probably a quantum critical point, is observed at around 19 GPa and, close to this pressure, the superconducting $T_{c}$ and the isothermal resistivity ($0<T<300\,$K) attain maximum values. In the superconducting pressure domain, the exponent $n = 5/3$ of the temperature power law of resistivity and its prefactor, which mimics $T_{c}$, indicate that ferromagnetic fluctuations may provide the glue for the Cooper pairs, yielding unconventional superconductivity

Rietveld refinement for indium nitride in the 105-295 K range

Results of Rietveld refinement for indium nitride data collected in the temperature range 105-295 K are presented. Acicular microcrystals of indium nitride prepared by reaction of liquid indium with nitrogen plasma were studied by X-ray diffraction. The diffraction measurements were carried out at the Swiss-Norwegian Beamline SNBL (ESRF) using a MAR345 image-plate detector. Excellent counting statistics allowed for refinement of the lattice parameters of InN as well as those of the metallic indium secondary phase. In the studied temperature range, the InN lattice parameters show a smooth increase that can be approximated by a linear function. Lattice-parameter dependencies confirm the trends indicated earlier by data measured using a conventional equipment. The relative change of both the a and c lattice parameters with increasing the temperature in the studied range is about 0.05%. The axial ratio slightly decreases with rising temperature. The experimental value of the free structural parameter, u=0.3769(14), is reported for InN for the first time. Its temperature variation is found to be considerably smaller than the experimental error. The thermal-expansion coefficients (TECs), derived from the linearly approximated lattice-parameter dependencies, are αa=3.09(14)×10−6 K−1 and αc=2.79(16)×10−6 K−1. The evaluated TECs are generally consistent with the earlier data. For the present dataset, the accuracy is apparently higher for both, the lattice parameters and thermal-expansion coefficients, than for the earlier results. The refined lattice parameter cIn of the indium secondary phase exhibits the known strongly nonlinear behavior; a shift (ΔT equal about −50 K) of the maximum in cIn(T) dependence is observed with respect to the literature dat

Computational Complexity of Synchronization under Regular Commutative Constraints

Here we study the computational complexity of the constrained synchronization problem for the class of regular commutative constraint languages. Utilizing a vector representation of regular commutative constraint languages, we give a full classification of the computational complexity of the constraint synchronization problem. Depending on the constraint language, our problem becomes PSPACE-complete, NP-complete or polynomial time solvable. In addition, we derive a polynomial time decision procedure for the complexity of the constraint synchronization problem, given some constraint automaton accepting a commutative language as input.Comment: Published in COCOON 2020 (The 26th International Computing and Combinatorics Conference); 2nd version is update of the published version and 1st version; both contain a minor error, the assumption of maximality in the NP-c and PSPACE-c results (propositions 5 & 6) is missing, and of incomparability of the vectors in main theorem; fixed in this version. See (new) discussion after main theore

Near-Optimal Scheduling for LTL with Future Discounting

We study the search problem for optimal schedulers for the linear temporal logic (LTL) with future discounting. The logic, introduced by Almagor, Boker and Kupferman, is a quantitative variant of LTL in which an event in the far future has only discounted contribution to a truth value (that is a real number in the unit interval [0, 1]). The precise problem we study---it naturally arises e.g. in search for a scheduler that recovers from an internal error state as soon as possible---is the following: given a Kripke frame, a formula and a number in [0, 1] called a margin, find a path of the Kripke frame that is optimal with respect to the formula up to the prescribed margin (a truly optimal path may not exist). We present an algorithm for the problem; it works even in the extended setting with propositional quality operators, a setting where (threshold) model-checking is known to be undecidable

Measuring the Process Parameters of the IBAD Method

Chromium nitride films are known as good protective layers for against both corrosion and wear. These coatings have been studied in detail during recent years. Their protective capability strongly depends on the deposition conditions. A modern method for preparing chromium nitride is the IBAD (Ion Beam Assisted Deposition) method. The main parameter determining the composition and properties of the films prepared by the IBAD method is the arrival ratio of impinging nitrogen ions to chromium atoms. In order to calibrate the ion beam XY-mechanical scanner with a Faraday cup, a detector was designed and constructed. By mathematical processing of the data, the flux of the nitrogen atoms was found. To obtain the flux of the chromium atoms the RBS and Talystep methods were used. Now, on the basis of this data, we can perform CrNx, coatings with controlled composition and properties

Reset thresholds of automata with two cycle lengths

We present several series of synchronizing automata with multiple parameters, generalizing previously known results. Let p and q be two arbitrary co-prime positive integers, q > p. We describe reset thresholds of the colorings of primitive digraphs with exactly one cycle of length p and one cycle of length q. Also, we study reset thresholds of the colorings of primitive digraphs with exactly one cycle of length q and two cycles of length p.Comment: 11 pages, 5 figures, submitted to CIAA 201

DLC Films Deposited by the DC PACVD Method

DLC (Diamond-Like Carbon) coatings have been suggested as protective surface layers against wear. However hard DLC coatings, especially those of greater thickness, have poor adhesion to substrates. We have used several ways to increase the adhesion of DLC coatings prepared by the PACVD (Plasma Assisted Chemical Vapour Deposition) method on steel substrates. One of these is the DC PACVD method for preparing DLC films