scholarly journals Multilayer heat equations: Application to finance

2021 ◽  
Vol 0 (0) ◽  
pp. 0
Author(s):  
Andrey Itkin ◽  
Alexander Lipton ◽  
Dmitry Muravey
Keyword(s):  
Finite Difference ◽  
Parabolic Equations ◽  
Mathematical Finance ◽  
Heat Equations ◽  
Barrier Options ◽  
Numerical Techniques ◽  
Quantitative Finance ◽  
The Core ◽  
Long Time ◽  
Short Rate Models

<p style='text-indent:20px;'>In this paper, we develop a Multilayer (ML) method for solving one-factor parabolic equations. Our approach provides a powerful alternative to the well-known finite difference and Monte Carlo methods. We discuss various advantages of this approach, which judiciously combines semi-analytical and numerical techniques and provides a fast and accurate way of finding solutions to the corresponding equations. To introduce the core of the method, we consider multilayer heat equations, known in physics for a relatively long time but never used when solving financial problems. Thus, we expand the analytic machinery of quantitative finance by augmenting it with the ML method. We demonstrate how one can solve various problems of mathematical finance by using our approach. Specifically, we develop efficient algorithms for pricing barrier options for time-dependent one-factor short-rate models, such as Black-Karasinski and Verhulst. Besides, we show how to solve the well-known Dupire equation quickly and accurately. Numerical examples confirm that our approach is considerably more efficient for solving the corresponding partial differential equations than the conventional finite difference method by being much faster and more accurate than the known alternatives.</p>

Leaving Agent-Relative Value Behind

Utilitas ◽  
2020 ◽  
pp. 1-15
Author(s):  
Christa M. Johnson
Keyword(s):  
Left Behind ◽  
The Core ◽  
Relative Value ◽  
Long Time ◽  
Commonsense Morality

Abstract Commonsense morality seems to feature both agent-neutral and agent-relative elements. For a long time, the core debate between consequentialists and deontologists was which of these features should take centerstage. With the introduction of the consequentializing project and agent-relative value, however, agent-neutrality has been left behind. While I likewise favor an agent-relative view, agent-neutral views capture important features of commonsense morality. This article investigates whether an agent-relative view can maintain what is attractive about typical agent-neutral views. In particular, I argue that the agent-relative reasons-wielding deontologist is ultimately able to capture those features ordinarily associated with agent-neutral views, while the agent-relative value wielding consequentialist is left with a dilemma. The consequentializer either succumbs to the concerns of her agent-neutral opponents or else abandons the distinctive and attractive features of her view. Either way, I conclude that agent-relative value is best left behind.

scholarly journals Positivity of solutions to the Cauchy problem for linear and semilinear biharmonic heat equations

2020 ◽  
Vol 10 (1) ◽  
pp. 353-370 ◽  
Author(s):  
Hans-Christoph Grunau ◽  
Nobuhito Miyake ◽  
Shinya Okabe
Keyword(s):  
Cauchy Problem ◽  
Initial Data ◽  
Fourth Order ◽  
Parabolic Equations ◽  
Sufficient Conditions ◽  
Nonlinear Parabolic Equations ◽  
Heat Equations ◽  
Cauchy Problems ◽  
The Cauchy Problem ◽  
Positivity Of Solutions

Abstract This paper is concerned with the positivity of solutions to the Cauchy problem for linear and nonlinear parabolic equations with the biharmonic operator as fourth order elliptic principal part. Generally, Cauchy problems for parabolic equations of fourth order have no positivity preserving property due to the change of sign of the fundamental solution. One has eventual local positivity for positive initial data, but on short time scales, one will in general have also regions of negativity. The first goal of this paper is to find sufficient conditions on initial data which ensure the existence of solutions to the Cauchy problem for the linear biharmonic heat equation which are positive for all times and in the whole space. The second goal is to apply these results to show existence of globally positive solutions to the Cauchy problem for a semilinear biharmonic parabolic equation.

Thermal Performance Evaluation of Cork Phenolic for Nozzle External Thermal Protection System Using 250 kW Plasma Jet Facility

2018 ◽  
Vol 140 (7) ◽  
Author(s):  
L. Aravindakshan Pillai ◽  
N. Sreenivas ◽  
K. Krishnaraj ◽  
Vinay Unnikrishnan ◽  
M. Ajith
Keyword(s):  
Thermal Performance ◽  
Thermal Protection ◽  
Plasma Jet ◽  
Thermal Protection System ◽  
Protection System ◽  
Convective Heating ◽  
Launch Vehicles ◽  
Time Of Application ◽  
The Core ◽  
Long Time

In one of the launch vehicles of ISRO, there are two solid strap-ons attached to the core liquid engine. During the ascent phase, the external nozzle divergent of the strap-ons experiences heating due to radiation from the strap-ons as well as convective heating from the impingement of plumes from the core engine. Hence, the nozzle divergent of the strap-on beyond compliance ring is thermally protected by a coating of PC10 insulation applied over carbon/epoxy structural backup. Though the system worked satisfactorily, application of PC10 had increased the inert weight of each nozzle by 165 kg and took long time for realization. To reduce the inert weight as well as the time of application, precast phenolic based cork sheets (CkP) having lower density than PC10 were selected, as a replacement to PC10. As part of evaluating the thermal performance of the CkP material, specimen level tests with different configurations were carried out in 250 kW plasma jet facility of Vikram Sarabhai Space Centre (VSSC) wherein both the heat flux and the shear stress as expected in flight were simulated simultaneously. At the end of the test program, CkP was found to be superior to PC10 for external thermal protection system (TPS). This paper highlights details of the qualification tests carried out for clearing the cork phenolic system for use in the future launches.

scholarly journals The Excess Secular Change in the Obliquity of the Ecliptic and Its Relation to the Internal Motion of the Earth

1972 ◽  
Vol 48 ◽  
pp. 192-195 ◽  
Author(s):  
Chuichi Kakuta ◽  
Shinko Aoki
Keyword(s):  
Time Variation ◽  
Rotational Speed ◽  
Internal Motion ◽  
Secular Change ◽  
Electrically Conducting ◽  
The Core ◽  
The Earth ◽  
Fluid Core ◽  
Electrical Conductivities ◽  
Long Time

The previous result (Aoki, 1969) on the explanation of the excess secular change in the obliquity of the ecliptic frictional couplings in the rigid constituents, the mantle and the core, is extended by using a model of an elastic and electrically conducting mantle and a hydromagnetic core. The secular change of the obliquity of the ecliptic referred to the mantle is found to be 1/3.2 times of the observed value, if the electrical conductivities of the fluid core and the mantle are assumed to be 3·10−6 emu and 3·10−9 emu respectively. A large secular deceleration of the Earth's rotational speed obtained in the previous result is proved to be strongly reduced because of weak excitation of the perturbing potential for a long time variation.

scholarly journals Expanded Microchannel Heat Exchanger: Finite Difference Modeling

Designs ◽  
2021 ◽  
Vol 5 (4) ◽  
pp. 58
Author(s):  
David Denkenberger ◽  
Joshua M. Pearce ◽  
Michael Brandemuehl ◽  
Mitchell Alverts ◽  
John Zhai
Keyword(s):  
Heat Transfer ◽  
Heat Exchanger ◽  
Finite Difference ◽  
Flow Rate ◽  
Experimental Results ◽  
Low Flow ◽  
Difference Model ◽  
The Core ◽  
Finite Difference Model ◽  
Flow Maldistribution

A finite difference model of a heat exchanger (HX) considered maldistribution, axial conduction, heat leak, and the edge effect, all of which are needed to model a high effectiveness HX. An HX prototype was developed, and channel height data were obtained using a computerized tomography (CT) scan from previous work along with experimental results. This study used the core geometry data to model results with the finite difference model, and compared the modeled and experimental results to help improve the expanded microchannel HX (EMHX) prototype design. The root mean square (RMS) error was 3.8%. Manifold geometries were not put into the model because the data were not available, so impacts of the manifold were investigated by varying the temperature conditions at the inlet and exit of the core. Previous studies have not considered the influence of heat transfer in the manifold on the HX effectiveness when maldistribution is present. With no flow maldistribution, manifold heat transfer increases overall effectiveness roughly as would be expected by the greater heat transfer area in the manifolds. Manifold heat transfer coupled with flow maldistribution for the prototype, however, causes a decrease in the effectiveness at high flow rate, and an increase in effectiveness at low flow rate.

scholarly journals Population, and its social and religious composition in Ivanovo and Yaroslavl regions on the eve of the Axis aggression against the USSR (according to the censuses of the USSR in 1937 and 1939)

2021 ◽  
Vol 27 (1) ◽  
pp. 74-78
Author(s):  
Natalya S. Maiorova
Keyword(s):  
World War Ii ◽  
Rural Areas ◽  
Urban Population ◽  
Daily Life ◽  
World War ◽  
Religious Policy ◽  
The Core ◽  
Long Time ◽  
High Level ◽  
Anxiety And Fear

The article is devoted to the analysis of the results of population censuses conducted in the USSR in 1937 and 1939, in relation to Ivanovo and Yaroslavl regions. The research is based on census materials that had been classified for a long time and published only in the 1990s. Of all the various aspects of the censuses, the author's attention was focused on only three – population, its social structure, and religious composition. Based on the results of the censuses, conclusions are drawn about the prevalence of women in the region, both in rural areas and in cities. It was women who, in the conditions of World War II, became the strong rear, on whose shoulders the front was supported by food, uniforms, and weapons. The urban population was greater in Ivanovo Region, which was explained by its characteristic high rates of industrialisation. The 1937 census recorded a fairly high level of religiosity, despite the largely anti-religious policy that had been carried out for almost 20 years. The war led to an increase in religiosity, probably because often only faith could become the core around which daily life was built, full of deprivation, anxiety and fear for loved ones.

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