On a stochastic differential equation arising in a price impact model

We provide sufficient conditions for the existence and uniqueness of solutions to a stochastic differential equation which arises in a price impact model. These conditions are stated as smoothness and boundedness requirements on utility functions or Malliavin differentiability of payoffs and endowments.Comment: 20 pages. Keywords: Clark-Ocone formula, large investor, Malliavin derivative, Pareto allocation, price impact, Sobolev's embedding, stochastic differential equation; a couple of minor editorial corrections to make it identical to the paper accepted to Stochastic Processes and Their Application

Integral representation of martingales motivated by the problem of endogenous completeness in financial economics

Let $\mathbb{Q}$ and $\mathbb{P}$ be equivalent probability measures and let $\psi$ be a $J$-dimensional vector of random variables such that $\frac{d\mathbb{Q}}{d\mathbb{P}}$ and $\psi$ are defined in terms of a weak solution $X$ to a $d$-dimensional stochastic differential equation. Motivated by the problem of \emph{endogenous completeness} in financial economics we present conditions which guarantee that every local martingale under $\mathbb{Q}$ is a stochastic integral with respect to the $J$-dimensional martingale S_t \set \mathbb{E}^{\mathbb{Q}}[\psi|\mathcal{F}_t]. While the drift $b=b(t,x)$ and the volatility $\sigma = \sigma(t,x)$ coefficients for $X$ need to have only minimal regularity properties with respect to $x$, they are assumed to be analytic functions with respect to $t$. We provide a counter-example showing that this $t$-analyticity assumption for $\sigma$ cannot be removed.Comment: A stronger version of the main theorem is obtained. The "financial" part of the previous version is remove

Reinforcement Learning Framework for Deep Brain Stimulation Study

Malfunctioning neurons in the brain sometimes operate synchronously, reportedly causing many neurological diseases, e.g. Parkinson's. Suppression and control of this collective synchronous activity are therefore of great importance for neuroscience, and can only rely on limited engineering trials due to the need to experiment with live human brains. We present the first Reinforcement Learning gym framework that emulates this collective behavior of neurons and allows us to find suppression parameters for the environment of synthetic degenerate models of neurons. We successfully suppress synchrony via RL for three pathological signaling regimes, characterize the framework's stability to noise, and further remove the unwanted oscillations by engaging multiple PPO agents.Comment: 7 pages + 1 references, 7 figures. arXiv admin note: text overlap with arXiv:1909.1215

Thermal Raman study of Li4Ti5O12 and discussion about the number of its characteristic bands

Lithium battery industry is booming, and this fast growth should be supported by developing industry friendly tools to control the quality of positive and negative electrode materials. Raman spectroscopy was shown to be a cost effective and sensitive instrument to study defects and heterogeneities in lithium titanate, popular negative electrode material for high power applications, but there are still some points to be clarified. This work presents a detailed thermal Raman study for lithium titanate and discusses the difference of the number of predicted and experimentally observed Raman-active bands. The low temperature study and the analysis of thermal shifts of bands positions during heating let us to conclude about advantages of the proposed approach with surplus bands and recommend using shifts of major band to estimate the sample heating

Master Robotic Net

The main goal of the MASTER-Net project is to produce a unique fast sky survey with all sky observed over a single night down to a limiting magnitude of 19 - 20mag. Such a survey will make it possible to address a number of fundamental problems: search for dark energy via the discovery and photometry of supernovas (including SNIa), search for exoplanets, microlensing effects, discovery of minor bodies in the Solar System and space-junk monitoring. All MASTER telescopes can be guided by alerts, and we plan to observe prompt optical emission from gamma-ray bursts synchronously in several filters and in several polarization planes.Comment: 10 pages, 8 figure

Geological structure of the northern part of the Kara Shelf near the Severnaya Zemlya archipelago according to recent studies

Until recently, the North of the Kara Shelf was completely unexplored by seismic methods. Seismic and seismo-acoustic data that have appeared in recent years have made it possible to decipher features of the regional geological structure. This study solves the urgent problem of determining the prospects for the oil and gas potential of the North Kara sedimentary basin. The relevance of the research is associated with determining the prospects of the oil and gas potential of the North Kara sedimentary basin. The aim of the study is to clarify the age of the reflecting horizons using data on the geology of the island, as well as to determine the tectonic position of the sedimentary cover and basement structures in the north of the Kara shelf. The sedimentary cover is divided into three structural levels: Cambrian-Devonian, Middle Carboniferous-Cretaceous, Miocene-Quarter. The Cambrian-Devonian complex fills the deep troughs of the North Kara shelf. The most noticeable discontinuity is the base of Carboniferous-Permian rocks, lying on the eroded surface of folded Silurian-Devonian seismic complexes. The blanket-like plate part of the cover is composed of thin Carbon-Quarter complexes. The authors came to the conclusion that the fold structures of the Taimyr-Severozemelskiy fold belt gradually degenerate towards the Kara sedimentary basin and towards the continental slope of the Eurasian basin of the Arctic Ocean. A chain of narrow uplifts within the seabed relief, which correspond to narrow anticlines is traced to the West of the Severnaya Zemlya islands. Paleozoic rocks have subhorizontal bedding further to the West, within the Kara shelf. Mesozoic folding in the North of the Kara Sea is expressed exclusively in a weak activation of movements along faults. At the neotectonic stage, the shelf near Severnaya Zemlya was raised and the Mesozoic complexes were eroded. The modern seismic activity of the North Zemlya shelf is associated with the ongoing formation of the continental margin

Soliton Squeezing in a Mach-Zehnder Fiber Interferometer

A new scheme for generating amplitude squeezed light by means of soliton self-phase modulation is experimentally demonstrated. By injecting 180-fs pulses into an equivalent Mach-Zehnder fiber interferometer, a maximum noise reduction of $4.4 \pm 0.3$ dB is obtained ($6.3 \pm 0.6$ dB when corrected for losses). The dependence of noise reduction on the interferometer splitting ratio and fiber length is studied in detail.Comment: 5 pages, 4 figure

Model of vocational school, high school and manufacture integration in the regional system of professional education

The article is aimed at the model development of vocational, high school and manufacture integration in the regional system of vocational education. The basic approach to the structural-functional model development of vocational, high school and manufacture integration in the regional system of vocational education is an integrative one, taking into consideration the integrated system ?vocational school-high school-manufacture? components in their unity and cooperation, giving it the integrity and structural and functional stability. Structural-functional model of vocational, high school and manufacture integration in the regional system of vocational education includes functional-target, organizational-structural, content, process and result components