A guaranteed deterministic approach to margining on exchange-traded derivatives market: Numerical experiment

2021 ◽  
Vol 57 (4) ◽  
pp. 76
Author(s):  
Sergey Smirnov
Keyword(s):  
Mathematical Model ◽  
Risk Management ◽  
Critical Role ◽  
Deterministic Approach ◽  
Computational Framework ◽  
Modern Approach ◽  
System A ◽  
Lipschitz Constants ◽  
Isaacs Equations ◽  
The Mathematical Model

The article discusses a modern approach to risk management of the central counterparty,primarily the issue of the sufficiency of its financial resources, including the provision of clearingmembers, the capital of the central counterparty and the mutual liability fund. The main subject is the margining system, responsible for an adequate level of collateral for clearing members, that plays critical role in risk management, being the vanguard in protecting against losses associated with default by clearing members and the most sensitive to market risk part of the central counterparty’s skin of the game. A system of margining a portfolio of options and futures in the derivatives market is described, with default management based on the methodology proposed by a number of inventors, registered in 2004. For this system, a mathematical model of margining (i.e. determining the required level of the collateral) is built, based on the ideology of a guaranteed deterministic approach to superhedging: Bellman–Isaacs equations are derived from the economic meaning of the problem. A form of these equations, convenient for calculations, is obtained. Lipschitz constants for the solutions of Bellman–Isaacs equations are estimated. A computational framework for efficient numerical solution of these equations is created. Numerical experiments are carried out on some model examples to demonstrate the efficiency of the system. These experiments also show practical implications of marginsubadditivity — a crucial property of the mathematical model.

scholarly journals Voice on quantitative methods in risk management by an air operator

2020 ◽  
Vol 109 ◽  
pp. 103-116
Author(s):  
Piotr MAKOWSKI
Keyword(s):  
Risk Factors ◽  
Mathematical Model ◽  
Risk Management ◽  
Quantitative Methods ◽  
Safety Management ◽  
Risk Matrix ◽  
Safety Risk ◽  
Assessment Indicator ◽  
Excursion Probability ◽  
The Mathematical Model

This article is devoted to the diagnosis of problems arising from risk management obligations under the safety management system implemented in civil organisations of certified air operators (carriers). Focus was on the use of quantitative methods in safety risk analysis. The idea of an approach to determine the probability of accidents and serious incidents based on the intensity of symptoms with lower consequences and risk factors as a function of time or number of performed air operations was proposed, based on Markov discrete processes [6,10-12,16]. The essence of this approach is explained by the mathematical model of Runway Excursion probability during landing operations. The concept of improvement of operators' cooperation in the exchange of information about safety indicators by profiling the organisation was presented. The last proposal concerns the construction of a comprehensive risk assessment indicator using a safety risk matrix.

scholarly journals Melacak Dampak Perubahan Iklim Terhadap Kondisi Makroekonomi dengan Teori Permainan Dinamis

2018 ◽  
Vol 7 (2) ◽  
pp. 57-62
Author(s):  
Muhammad Wakhid Musthofa
Keyword(s):  
Climate Change ◽  
Economic Growth ◽  
Mathematical Model ◽  
Equation System ◽  
Output Function ◽  
Macroeconomic Conditions ◽  
System A ◽  
Economic Growth Model ◽  
The Impact ◽  
The Mathematical Model

Makalah ini membahas tentang model matematika dampak perubahan iklim terhadap kondisi makroekonomi suatu negara. Dengan mengacu pada model pertumbuhan ekonomi endogen pada suatu negara, dengan fungsi output berbentuk fungsi Cobb-Douglas akan diturunkan model matematika yang mendeskripsikan dampak perubahan iklim terhadap kondisi makroekonomi suatu negara. Selanjutnya, akan dikonstruksikan pula fungsi ongkos yang berhubungan dengan model matematika yang telah diturunkan. Mengingat model matematika tersebut masih dalam bentuk sistem persamaan nonlinear, maka diperlukan proses linearisasi untuk menghasilkan model matematika yang linear sehingga memudahkan untuk dianalisis maupun diaplikasikan. [This paper discusses the mathematical model of the impact of climate change on the macroeconomic conditions of a country. By referring to an endogenous economic growth model in a country, with the output function in the form of a Cobb-Douglas function, a mathematical model will be described that describes the effects of climate change on the macroeconomic conditions of a country. Furthermore, it will also construct cost functions related to mathematical models that have been derived. Considering that the mathematical model is still in the form of a nonlinear equation system, a linearisation process is needed to produce a linear mathematical model that makes it easy to analyze and apply.]

Modeling and Simulation of pH Dependent Isotachophoresis

2009 ◽  
Author(s):  
Jaesool Shim ◽  
Prashanta Dutta ◽  
Cornelius F. Ivory
Keyword(s):  
Mathematical Model ◽  
Mass Conservation ◽  
Microfluidic System ◽  
Band Broadening ◽  
System A ◽  
Band Dispersion ◽  
Electroneutrality Condition ◽  
Ph Dependent ◽  
The Mathematical Model ◽  
Ionic Components

This paper presents a mathematical model for pH gradient ITP in a microfluidic system. The mathematical model is based on mass conservation, charge conservation and electroneutrality condition in the system. A finite volume based numerical model is developed to simulate pH dependent isotachophoresis (ITP) in microfluidic devices. Numerical results of pH dependent ITP are obtained for straight and dog-leg microchannels. For both channels, five ionic components are used to simulate the model ITP system. The ITP results obtained from dog-leg microchannel capture the band broadening and band dispersion observed in T-channel junction. However, no such dispersion is noticed for ITP in the straight microchannel.

Research of Mathematical Model of the Twelve-Phase Linear Induction Motor with Double-Sided Long Stators

2013 ◽  
Vol 416-417 ◽  
pp. 156-163 ◽  
Author(s):  
Jin Rao ◽  
Jin Xu ◽  
De Zhi Liu ◽  
Xi Dang Yang ◽  
Xiao Peng Cui ◽  
...  
Keyword(s):  
Mathematical Model ◽  
Induction Motor ◽  
Electromagnetic Properties ◽  
Linear Induction ◽  
Linear Induction Motor ◽  
Leakage Inductance ◽  
System A ◽  
The Asymmetry ◽  
Multi Phase ◽  
The Mathematical Model

Based on the requirement of high-power linear propulsion system, a novel twelve-phase linear induction motor (LIM) with double-sided long stators was designed, and the winding construction of twelve-phase LIM was presented in this paper. On the basis of this, the mathematical model of ABC coordinates for this novel motor was derived, and the rule of the asymmetry of end-winding leakage inductance of the twelve-phase LIM with double-sided long stators, which is determined by the relative space position of the each phase end-winding in the motor, and then this rule was compared with the law of the asymmetry of end-winding leakage inductance of the multi-phase rotating motor. Simulation model of the motor was established, and the electromagnetic properties of the motor is calculated.

scholarly journals RECONNAISSANCE MICRO UAV SYSTEM

2015 ◽  
Vol 2 (2) ◽  
pp. 15-21 ◽  
Author(s):  
Petr Gabrlik ◽  
Vlastimil Kriz ◽  
Ludek Zalud
Keyword(s):  
Mathematical Model ◽  
Control System ◽  
Communication Protocol ◽  
Robotic System ◽  
Design And Implementation ◽  
System A ◽  
Flying Robot ◽  
The Mathematical Model

This paper describes the design and implementation of the Uranus UAV. This quad-rotor flying robot was created to extend the abilities of the hitherto developed with airborne missions. The first part deals with the mathematical model of the robot. Next, the control system is designed, and the proposed hardware as well as the implemented software solution are presented. For integration into the robotic system, a new communication protocol was created and is described here too.

scholarly journals A mathematical investigation of different growth rates in simultaneous tumors at two distant sites

2021 ◽  
Author(s):  
Farjana Aktar
Keyword(s):  
Mathematical Model ◽  
Growth Rate ◽  
Simulated Annealing Algorithm ◽  
The Other ◽  
Sensitivity Analyses ◽  
Small Tumour ◽  
System A ◽  
Set Up ◽  
Parameter Values ◽  
The Mathematical Model

Experimental data demonstrates that simultaneous injection of cancer cells at two distinct sites often results in one large and one small tumour. Unbalanced tumour-stimulating inflammation is hypothesized to be the cause of this growth rate separation, causing one tumour to grow faster than the other. Here, a mathematical model for immune recruitment and competition between two cancer sites is developed to explore the role of tumour-promoting inflammation in the observed growth rate separation. Due to the experimental set-up, immune predation may be neglected, focusing the model on tumour-promoting immune actions. A new mathematical model with localized immune recruitment and competition between the two cancer sites is developed using a multi-compartment ODE system. A simulated annealing algorithm is used to fit the model to control data (one tumour burden). Stability and parameter sensitivity analyses are used to explore the mathematical model and parameter space. Next, the two-tumour scenario is predicted by testing parameter values tied to possible biological mechanisms of action. The model predicts that indeed inflammation may be a contributor to growth rate separation observed in simultaneous tumour growth, if one site is pre-inflamed compared to the other.

Numerical analysis of fractional-order tumor model

2015 ◽  
Vol 08 (05) ◽  
pp. 1550069 ◽  
Author(s):  
Ayesha Sohail ◽  
Sadia Arshad ◽  
Sana Javed ◽  
Khadija Maqbool
Keyword(s):  
Mathematical Model ◽  
Immune Response ◽  
Fractional Order ◽  
Interleukin 2 ◽  
Tumor Model ◽  
Graphical Analysis ◽  
System A ◽  
The Stability ◽  
The Mathematical Model ◽  
Limiting Values

In this paper, the tumor-immune dynamics are simulated by solving a nonlinear system of differential equations. The fractional-order mathematical model incorporated with three Michaelis–Menten terms to indicate the saturated effect of immune response, the limited immune response to the tumor and to account the self-limiting production of cytokine interleukin-2. Two types of treatments were considered in the mathematical model to demonstrate the importance of immunotherapy. The limiting values of these treatments were considered, satisfying the stability criteria for fractional differential system. A graphical analysis is made to highlight the effects of antigenicity of the tumor and the fractional-order derivative on the tumor mass.

scholarly journals TO THE QUESTION OF OPTIMISING THE DYNAMIC CHARACTERISTICS OF A VIBRATIONAL TREE UPROOTING MACHINE

2018 ◽  
Vol 45 (2) ◽  
pp. 149-157
Author(s):  
A. R. Mikhitarov ◽  
V. L. Savich ◽  
V. K. Khegai
Keyword(s):  
Mathematical Model ◽  
Root System ◽  
Dynamic Characteristics ◽  
Mutual Influence ◽  
Frequency Characteristics ◽  
Frequency Range ◽  
System A ◽  
Forest Sites ◽  
Tree Uprooting ◽  
The Mathematical Model

Objectives Following logging operations, tree stumps remain in the site of the former forest.While these may be uprooted by special machines in the course of forestry operations, the use of heavy forestry machines operated repeatedly on the forest sites not only lead to soil erosion, but also to considerable financial expense. Consequently, the development of machines combining cutting (logging) and uprooting operations – that is, uprooting the trees along with their roots – are of a great interest. As research has shown, the main disadvantages of the use of such technology by “conventional” logging or forestry machines are their excessive loading and energy intensity. The aim of the research is to investigate means of eliminating these drawbacks by using vibration.Methods The article deals with theproblem of ensuring the effectiveness of the vibration application – in particular, torsional vibrations, used to stub trees together with their roots. To solve this problem, a mathematical model of the “machine-tree-soil-root system” system was developed, which takes into account the mutual influence of the dynamic characteristics of the machine’s technological equipment and tree and soil-root system, which allows a rational (optimal) frequency range of vibration equipment to be selected by analysing the amplitude-frequency characteristics of a given system. To analyse the amplitude-frequency characteristics of a mechanical system, the Euler-Lagrange equationswere used.Results Based on the mathematical model of the “machine-tree-soil-root system (SRS)” system and an analysis of the amplitude-frequency characteristics of a given system, a rational range of vibration frequencies was determined. As shown by analysis, the work of vibrational equipment in a given frequency range can significantly reduce the dynamic loading of the machine and at the same time create appropriate conditions for the effective destruction of the soil-root system.Conclusion The proposed method allows the rational values of the frequency characteristic of vibration equipment for each calculated tree to be found depending on the soil type and the basic machine.

scholarly journals Feasibility study of logging road elements plan

2021 ◽  
Vol 25 (3) ◽  
pp. 111-117
Author(s):  
S.Yu. Sablin ◽  
◽  
A.V. Skrypnikov ◽  
V.G. Kozlov ◽  
V.S. Prokopets ◽  
...  
Keyword(s):  
Mathematical Model ◽  
Objective Function ◽  
Feasibility Study ◽  
Research Work ◽  
Operating Costs ◽  
System A ◽  
Reduced Costs ◽  
Geometric Elements ◽  
The Mathematical Model ◽  
Further Development

The peculiarities of the research work are stated and the need for its further development is shown. Taking into account the structural links and limitations of the system, a mathematical model of the feasibility study of the total reduced costs of the route plan, the longitudinal profile and the width of the carriageway was compiled, which has a various amount of construction and operating costs reduced to the initial year in a predetermined search area. The objective function is determined, which is the main part of the mathematical model including all the elements and connections of the feasibility study of the timber haul roads elements. It is concluded that the search for the optimal combination of geometric elements and the timing of their change is an extreme task, and the best method for solving it is to determine the state of the system corresponding to the minimum value of the objective function, which is the sum of construction and operating costs reduced to the initial year.

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