Study of the risk-adjusted pricing methodology model with methods of Geometrical Analysis

Families of exact solutions are found to a nonlinear modification of the Black-Scholes equation. This risk-adjusted pricing methodology model (RAPM) incorporates both transaction costs and the risk from a volatile portfolio. Using the Lie group analysis we obtain the Lie algebra admitted by the RAPM equation. It gives us the possibility to describe an optimal system of subalgebras and correspondingly the set of invariant solutions to the model. In this way we can describe the complete set of possible reductions of the nonlinear RAPM model. Reductions are given in the form of different second order ordinary differential equations. In all cases we provide solutions to these equations in an exact or parametric form. We discuss the properties of these reductions and the corresponding invariant solutions.Comment: larger version with exact solutions, corrected typos, 13 pages, Symposium on Optimal Stopping in Abo/Turku 200

Nonlinear Parabolic Equations arising in Mathematical Finance

This survey paper is focused on qualitative and numerical analyses of fully nonlinear partial differential equations of parabolic type arising in financial mathematics. The main purpose is to review various non-linear extensions of the classical Black-Scholes theory for pricing financial instruments, as well as models of stochastic dynamic portfolio optimization leading to the Hamilton-Jacobi-Bellman (HJB) equation. After suitable transformations, both problems can be represented by solutions to nonlinear parabolic equations. Qualitative analysis will be focused on issues concerning the existence and uniqueness of solutions. In the numerical part we discuss a stable finite-volume and finite difference schemes for solving fully nonlinear parabolic equations.Comment: arXiv admin note: substantial text overlap with arXiv:1603.0387

The impact of the orifice plate deformation on the differential pressure value

This work aims to determine the impact of orifice plate deformation on the differential pressure at the high-pressure natural gas pipelines. The article focuses on the differences of the pressure values, velocity values and flow directions between deformed and undeformed orifice plate. The article contains deformation analysis of the orifice plate and CFD simulations of flowing natural gas through the orifice plates. CFD simulations contain basic models of the turbulence for both types of orifice plate. Whole research is based on the elimination of the negative influence of the deformation on the precise flow measuring of natural gas at the high-pressure pipelines

Utylizacja materiałów z rolnictwa do produkcji peletów

Wood pellets without bark are increasingly popular. Their greatest positives include a high degree of operating comfort, low ash content and low emission CO, NOx, SO2, OGC, PM production during combustion. Their main negative is the high production cost. One option to reduce the price of pellets is the production of pellets from waste products from agriculture. As starting material, there may be used different types of biomass, such straw, grass and various organic materials. Price of alternative pellets may be half of wood pellets price. Properties of alternative pellets are worse in comparison with wood pellets. The article deals about utilization of different types of biomass for pellets production. In this experimental work were made 4 types of pellets – from spruce wood without bark content (reference sample), miscanthus giganteus, wheat straw and rape straw. There were tested several properties of pellets samples: total heating value (calorific value), amount of fines, mechanical durability, water resistance and ash content. The results confirmed that wood pellets have the highest quality, but alternative pellets can be interesting cheaper choice to wood pellets, if consumer is satisfied with worse parameters.Drzewne pelety bez kory są coraz bardziej popularne. Ich największymi zaletami są: wysoki komfort obsługi, niska zawartość popiołu oraz niska produkcja emisji CO, NOx, SO2, OGC, PM podczas spalania. Ich główną wadą jest wysoki koszt produkcji. Jedną z opcji zmniejszenia ceny peletów jest produkcja peletów z produktów odpadowych, pochodzących z rolnictwa. Jako wstępne materiały mogą być wykorzystane różne typy biomasy: słoma, trawa oraz różne organiczne materiały. Cena alternatywnych peletów może być połowiczna w porównaniu z ceną peletów drzewnych. Z kolei właściwości peletów alternatywnych są gorsze w porównaniu z peletami drzewnymi. Artykuł dotyczy wykorzystania różnych typów biomasy do produkcji peletów. W pracy wyprodukowano eksperymentalnie 4 rodzaje peletów: z trocin drzewnych świerkowych bez kory (referencyjna próba), ze słomy pszenicznej oraz ze słomy rzepakowej, a także z miskanta olbrzymiego. Testowano kilka właściwości peletów: całkowite ciepło spalania (wartość opałowa), zawartość drobnych cząstek, mechaniczną wytrzymałość, wodoodporność oraz zawartość popiołu. Wyniki badań potwierdziły, że drzewne pelety osiągają najwyższą jakość, ale alternatywne pelety mogą stanowić tańszą opcja dla drzewnych peletów, jeśli konsument jest zadowolony z gorszych właściwości

The impact of the orifice plate deformation on the differential pressure value

This work aims to determine the impact of orifice plate deformation on the differential pressure at the high-pressure natural gas pipelines. The article focuses on the differences of the pressure values, velocity values and flow directions between deformed and undeformed orifice plate. The article contains deformation analysis of the orifice plate and CFD simulations of flowing natural gas through the orifice plates. CFD simulations contain basic models of the turbulence for both types of orifice plate. Whole research is based on the elimination of the negative influence of the deformation on the precise flow measuring of natural gas at the high-pressure pipelines

Influence of volume working fluid and ambient temperature on cooling efficiency of loop thermosyphon

Article deal with research of device for electrical component cooling used to heat transfer working fluid phase change. Amount of heat flux transferred by thermosyphon loop depend from amount working fluid and from ambient temperature where is heat removal too. In article is described proposal construction of thermosyphon loop, comparisons of his cooling efficiency if is filled 40 % and 50 % volume of working fluid and condenser (ambient) temperature from 20, 30 up to 40 °C at heat load from 40 to 360 W

Wybrane naukowe i inżynierskie zastosowania techniki termowizyjnej

The paper presents applications in infrared measurements. It discusses the use of thermovision in the analysis of heat losses in buildings, environmental monitoring, scientific research in thermal fields on different surfaces and other. Examples of the infrared measurements are given and discussed in the text

Experimental determination of the working fluid volume for optimal function of the loop heat pipe

This experiment is concentrated on the working fluid of the heat pipe. The working fluid is an important part for the function of the heat pipe regarding the transfer of the heat. The measurements point out the appropriate quantity of the working fluid regarding the correct function of the loop heat pipe in the cooling of electronic components

Staged the conversion of carbon dioxide in the simulator

The article described the transmission of low-potential heat measurement carried out on the simulator by using the thermal tube heat exchanger into the Earth. On this Simulator is carried out the research of transmission phenomena at different temperature parameters of temperature and pressure at the inlet to the Simulator and the various parameters of the carbon dioxide, such as the working substances in thermal tube. In the article will be referred to the conclusions arising from experimental measurements on the transmission of low-potential heat and their analysis of the Simulator, as well as the particulars of the theoretical phase of carbon dioxide in thermal tube, depending on the variations in pressure and temperature. While the impact of these two variables will be analyzed for other parameters of the system, such as an input and an output temperature of the coolant in the heat exchanger and the cooling of the surrounding rocks