scholarly journals Directional Stochastic Orders with an Application to Financial Mathematics

Mathematics ◽  
2021 ◽  
Vol 9 (4) ◽  
pp. 380
Author(s):  
María Concepción López-Díaz ◽  
Miguel López-Díaz ◽  
Sergio Martínez-Fernández
Keyword(s):  
Mathematical Model ◽  
Finite Number ◽  
Cash Flows ◽  
Stochastic Orders ◽  
Financial Mathematics ◽  
New Class ◽  
Unified Study ◽  
Relevant Role ◽  
Increasing Functions

Relevant integral stochastic orders share a common mathematical model, they are defined by generators which are made up of increasing functions on appropriate directions. Motivated by the aim to provide a unified study of those orders, we introduce a new class of integral stochastic orders whose generators are composed of functions that are increasing on the directions of a finite number of vectors. These orders will be called directional stochastic orders. Such stochastic orders are studied in depth. In that analysis, the conical combinations of vectors in those finite subsets play a relevant role. It is proved that directional stochastic orders are generated by non-stochastic pre-orders and the class of their preserving mappings. Geometrical characterizations of directional stochastic orders are developed. Those characterizations depend on the existence of non-trivial subspaces contained in the set of conical combinations. An application of directional stochastic orders to the field of financial mathematics is developed, namely, to the comparison of investments with random cash flows.

The inverse problem of recovering the coefficients of a differential equations on a graph

2020 ◽  
Vol 28 (5) ◽  
pp. 727-738
Author(s):  
Victor Sadovnichii ◽  
Yaudat Talgatovich Sultanaev ◽  
Azamat Akhtyamov
Keyword(s):  
Inverse Problem ◽  
Inverse Problems ◽  
Differential Equations ◽  
Boundary Value Problem ◽  
Boundary Conditions ◽  
Finite Number ◽  
Characteristic Equation ◽  
Arbitrary Number ◽  
New Class ◽  
Finite Set

AbstractWe consider a new class of inverse problems on the recovery of the coefficients of differential equations from a finite set of eigenvalues of a boundary value problem with unseparated boundary conditions. A finite number of eigenvalues is possible only for problems in which the roots of the characteristic equation are multiple. The article describes solutions to such a problem for equations of the second, third, and fourth orders on a graph with three, four, and five edges. The inverse problem with an arbitrary number of edges is solved similarly.

scholarly journals MODELING AND PRODUCTIVITY PREDICTION OF THE COMPANIES-INTERNAL CROWDSOURCING-BASED IDEATION

2021 ◽  
Vol 1 ◽  
pp. 2147-2156
Author(s):  
Pavel Livotov
Keyword(s):  
Mathematical Model ◽  
Finite Number ◽  
Research Question ◽  
Performance Function ◽  
Non Linear ◽  
Series Of Experiments ◽  
Productivity Prediction ◽  
A Company

AbstractThe internal crowdsourcing-based ideation within a company can be defined as an involvement of its staff, specialists, managers, and other employees, to propose solution ideas for a pre-defined problem. This paper addresses a question, how many participants of the company-internal ideation process are required to nearly reach the ideation limit for the problems with a finite number of workable solutions. To answer the research question, the author proposes a set of metrics and a non-linear ideation performance function with a positive decreasing slope and ideation limit for the closed-ended problems. Three series of experiments helped to explore relationships between the metric attributes and resulted in a mathematical model which allows companies to predict the productivity metrics of their crowdsourcing ideation activities such as quantity of different ideas and ideation limit as a function of the number of contributors, their average personal creativity and ideation efficiency of a contributors’ group.

Damping and Bandgap Characteristics of a Viscoelastic Tensegrity Damper

2021 ◽  
pp. 1-47
Author(s):  
Mohamed Raafat ◽  
Amr Baz
Keyword(s):  
Mathematical Model ◽  
Material Characterization ◽  
Structural Vibrations ◽  
New Class ◽  
Structural Applications ◽  
Theoretical Predictions ◽  
Specific Frequency ◽  
The Mathematical Model ◽  
Theory And Experiments

Abstract A theoretical and experimental investigation of a new class of a tensegrity-based structural damper is presented. The damper is not only capable of attenuating undesirable structural vibrations, as all conventional dampers, but also capable of completely blocking the transmission of vibration over specific frequency bands by virtue of its periodicity. Such dual functionality distinguishes the tensegrity damper over its counterparts of existing structural dampers. Particular emphasis is placed here in presenting the concept and developing the mathematical model of the dynamics of a unit cell the damper. The model is then coupled with a Floquet-Bloch analysis in order to identify the bandgap characteristics of the damper. The predictions of the mathematical model are validated experimentally using a prototype of the damper which is built using 3D printing. A comprehensive material characterization of the damper is performed followed by a detailed extraction of the static and dynamic behavior of the damper in order to validate the theoretical predictions. Close agreement is observed between theory and experiments. The developed theoretical and experimental techniques provide invaluable means for the design of this new class of dampers particularly for critical structural applications.

A branch & cut/metaheuristic optimization of financial supply chain based on input-output network flows: investigating the iranian orthopedic footwear

2021 ◽  
pp. 1-19
Author(s):  
Peide Liu ◽  
Ayad Hendalianpour
Keyword(s):  
Mathematical Model ◽  
Supply Chain ◽  
Network Flows ◽  
Cash Flows ◽  
Financial Flows ◽  
Conflicting Objectives ◽  
Financial Flow ◽  
Corporate Profits ◽  
Payment Mechanisms

Financial flows are one of the three majors in a Supply Chain (SC). Ignoring financial flows, regardless of the quality of freight transport and information, could lead the organization to a state of bankruptcy, which is a situation directly resulting from a lack of control over financial inputs/outputs. This study proposes a multi-product mathematical model, which makes it possible to choose among suppliers, manufacturing sites, distribution centres, retailers, and transportation vehicles. The purpose of the model is to integrate physical and material dimensions to maximize net corporate profits through inbound and outbound financial flows; it involves payment mechanisms between the financial and physical flows through maximizing the cash flows of manufacturing sites and suppliers, as two conflicting objectives that must consider the reciprocal effects of their decisions. These objectives are calculated by subtracting costs from the revenue; this process, of course, will ultimately result in an optimization of the organization’s financial flow. To solve the proposed mathematical model, the study relies on two algorithms, namely Particle Swarm Optimization (PSO) and Imperialist Competition Algorithm (ICA). The sample under investigation is solved separately using the three algorithms, and results are then compared. The observations of the study reveal the better performance of PSO.

scholarly journals The issue of loading the material in a vibro-impact grinder

2019 ◽  
Vol 109 ◽  
pp. 00024 ◽  
Author(s):  
Olena Fedoskina ◽  
Valerii Fedoskin ◽  
Anastasiia Loginova
Keyword(s):  
Mathematical Model ◽  
Phase Angle ◽  
Basic Principles ◽  
Working Chamber ◽  
Force Loading ◽  
New Class ◽  
Power Loading ◽  
The Moment ◽  
Rotational Oscillations

The article discusses the basic principles of force loading of a material in a vibro-impact grinder with a vertical and inclined working chamber. It is shown that in a grinder with a vertical working chamber the control of the material loading is limited by the presence of a relationship between the vertical and rotational oscillations of the jaws. Vibro-impact grinder with an inclined working chamber represents a new class of machines. A mathematical model of the process of interaction of the jaw with a piece of material when moving it in the working chamber is presented. Equations and graphical dependencies are obtained, which determine the phase angle of the moment of clamping the piece in the working chamber. The modes of power loading of the material in the working chamber were analyzed.

Stochastic Orders Generated by Integrals: a Unified Study

1997 ◽  
Vol 29 (02) ◽  
pp. 414-428 ◽  
Author(s):  
Alfred Müller
Keyword(s):  
Functional Analysis ◽  
Weak Convergence ◽  
Likelihood Ratio ◽  
Stochastic Orders ◽  
Probability Measures ◽  
Likelihood Ratio Order ◽  
Unified Study ◽  
Maximal Cone ◽  
Class Of Functions

We consider stochastic orders of the following type. Let be a class of functions and let P and Q be probability measures. Then define , if ∫ ⨍ d P ≦ ∫ ⨍ d Q for all f in . Marshall (1991) posed the problem of characterizing the maximal cone of functions generating such an ordering. We solve this problem by using methods from functional analysis. Another purpose of this paper is to derive properties of such integral stochastic orders from conditions satisfied by the generating class of functions. The results are illustrated by several examples. Moreover, we show that the likelihood ratio order is closed with respect to weak convergence, though it is not generated by integrals.

Stochastic Orders Generated by Integrals: a Unified Study

1997 ◽  
Vol 29 (2) ◽  
pp. 414-428 ◽  
Author(s):  
Alfred Müller
Keyword(s):  
Functional Analysis ◽  
Weak Convergence ◽  
Likelihood Ratio ◽  
Stochastic Orders ◽  
Probability Measures ◽  
Likelihood Ratio Order ◽  
Unified Study ◽  
Maximal Cone ◽  
Class Of Functions

We consider stochastic orders of the following type. Let be a class of functions and let P and Q be probability measures. Then define , if ∫ ⨍ d P ≦ ∫ ⨍ d Q for all f in . Marshall (1991) posed the problem of characterizing the maximal cone of functions generating such an ordering. We solve this problem by using methods from functional analysis. Another purpose of this paper is to derive properties of such integral stochastic orders from conditions satisfied by the generating class of functions. The results are illustrated by several examples. Moreover, we show that the likelihood ratio order is closed with respect to weak convergence, though it is not generated by integrals.

scholarly journals WAVES GENERATED BY A PISTON-TYPE WAVEMAKER

1970 ◽  
Vol 1 (12) ◽  
pp. 36 ◽  
Author(s):  
Ole Secher Madsen
Keyword(s):  
Mathematical Model ◽  
Finite Number ◽  
Wave Height ◽  
Finite Amplitude ◽  
Governing Equations ◽  
Approximate Evaluation ◽  
Large Wave ◽  
Wave Heights ◽  
The Waves ◽  
Theoretical Results

When a wavemaker generates a finite number of waves, it has been found that one of the first and one of the last waves in such a burst is considerably larger than the average A mathematical model, based on the linearized governing equations, is used for the particular problem of the waves generated by a sinusoidally moving piston-type wavemaker starting from rest Theoretical results for the magnitude of the large wave relative to the average agree fairly well with experiments, however, the actual wave height is smaller in the experiments than predicted by theory It is shown, by extending the classical wavemaker theory to second order, that finite amplitude effects do not offer an explanation However, pistons rarely fit the tank dimensions exactly, and an approximate evaluation indicates that the discrepancy between predicted and observed wave heights can be attributed to the effects of leakage around the piston.

scholarly journals Rational Savings Account Models for Backward-Looking Interest Rate Benchmarks

Risks ◽  
2020 ◽  
Vol 8 (1) ◽  
pp. 23 ◽  
Author(s):  
Andrea Macrina ◽  
David Skovmand
Keyword(s):  
Interest Rate ◽  
Cash Flows ◽  
Rate System ◽  
Rational Form ◽  
Adjusted Risk ◽  
New Class ◽  
Discount Factors ◽  
Major Transition ◽  
Risk Free Rate ◽  
High Degree

Interest rate benchmarks are currently undergoing a major transition. The LIBOR benchmark is planned to be discontinued by the end of 2021 and superseded by what ISDA calls an adjusted risk-free rate (RFR). ISDA has recently announced that the LIBOR replacement will most likely be constructed from a compounded running average of RFR overnight rates over a period matching the LIBOR tenor. This new backward-looking benchmark is markedly different when compared with LIBOR. It is measurable only at the end of the term in contrast to the forward-looking LIBOR, which is measurable at the start of the term. The RFR provides a simplification because the cash flows and the discount factors may be derived from the same discounting curve, thus avoiding—on a superficial level—any multi-curve complications. We develop a new class of savings account models and derive a novel interest rate system specifically designed to facilitate a high degree of tractability for the pricing of RFR-based fixed-income instruments. The rational form of the savings account models under the risk-neutral measure enables the pricing in closed form of caplets, swaptions and futures written on the backward-looking interest rate benchmark.

GAUGE MODELS OF FERMIONIC DISCRETE "STRINGS"

1990 ◽  
Vol 05 (05) ◽  
pp. 325-335 ◽  
Author(s):  
A.T. FILIPPOV ◽  
A.P. ISAEV
Keyword(s):  
String Theory ◽  
Finite Number ◽  
Degrees Of Freedom ◽  
Independent Variables ◽  
Gauge Models ◽  
New Class ◽  
Constrained Hamiltonian Systems ◽  
New Models ◽  
Fermionic String ◽  
Left And Right

A new class of constrained hamiltonian systems with a finite number of bosonic and fermionic degrees of freedom is proposed. Coordinates of these systems are divided into two groups of independent variables analogous to the left and right movers of the standard closed fermionic string theory. Hamiltonians are obtained by gauging some subgroups of the linear supercanonical transformations for the left and right variables. It is argued that some of the new models can be regarded as discrete analogs of the standard fermionic string theory. The extension of the models obtained by adding ghost variables is also constructed as a prerequisite to quantizing them.

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