Inverse problem and concentration method of a continuous-in-time financial model

In a continuous-in-time model, there is an important financial quantity called Loan which cannot be determined directly in terms of algebraic spending but has a major impact on the financial strategy. In this paper, we use a mathematical framework to discuss an inverse problem of determining the implied Loan Measure from Algebraic Spending Measure when it is possible. In addition, we build a numerical method to concentrate a measure as a sum of Dirac masses.

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Some Notes about the Continuous-in-Time Financial Model

Abstract and Applied Analysis ◽

10.1155/2017/6985820 ◽

2017 ◽

Vol 2017 ◽

pp. 1-11 ◽

Cited By ~ 1

Author(s):

Tarik Chakkour

Keyword(s):

Inverse Problem ◽

Uniqueness Theorem ◽

Schwartz Space ◽

Public Institutions ◽

Financial Model ◽

Time Model ◽

The Uniqueness Theorem

In this paper, we investigate the properties of operators in the continuous-in-time model which is designed to be used for the finances of public institutions. These operators are involved in the inverse problem of this model. We discuss this inverse problem in Schwartz space that we prove the uniqueness theorem.

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Numerical method of identification of an unknown source term in a heat equation

Mathematical Problems in Engineering ◽

10.1080/10241230212907 ◽

2002 ◽

Vol 8 (2) ◽

pp. 161-168 ◽

Cited By ~ 2

Author(s):

Afet Golayoğlu Fatullayev

Keyword(s):

Inverse Problem ◽

Heat Equation ◽

Numerical Method ◽

Minimization Problem ◽

Unknown Function ◽

Source Term ◽

Numerical Procedure ◽

Numerical Examples ◽

Unknown Source

A numerical procedure for an inverse problem of identification of an unknown source in a heat equation is presented. Approach of proposed method is to approximate unknown function by polygons linear pieces which are determined consecutively from the solution of minimization problem based on the overspecified data. Numerical examples are presented.

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A Numerical Method to Solve a Phaseless Coefficient Inverse Problem from a Single Measurement of Experimental Data

SIAM Journal on Imaging Sciences ◽

10.1137/18m1179560 ◽

2018 ◽

Vol 11 (4) ◽

pp. 2339-2367 ◽

Cited By ~ 7

Author(s):

Michael V. Klibanov ◽

Nikolay A. Koshev ◽

Dinh-Liem Nguyen ◽

Loc H. Nguyen ◽

Aaron Brettin ◽

...

Keyword(s):

Experimental Data ◽

Inverse Problem ◽

Numerical Method ◽

Coefficient Inverse Problem ◽

Single Measurement

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DEFINITION OF HYDRAULIC RESISTANCE OF UNDERGROUND OIL PIPELINE

Bulletin Series of Physics & Mathematical Sciences ◽

10.51889/2020-1.1728-7901.09 ◽

2020 ◽

Vol 69 (1) ◽

pp. 56-61

Author(s):

L. Yermekkyzy ◽

Keyword(s):

Heat Transfer ◽

Inverse Problem ◽

Numerical Method ◽

Hydraulic Resistance ◽

High Viscosity ◽

System Of Equations ◽

Oil Viscosity ◽

Oil Pipeline ◽

Conservation Of Momentum ◽

Definition Of

The results of solving the inverse problem of determining the hydraulic resistance of a main oil pipeline are presented. The formulation of the inverse problem is formulated, a numerical method for solving the system of equations is described. The hydraulic resistance of the pipeline during the "hot" pumping of high-curing and high-viscosity oil changes during operation. Oil temperature decreases along the length of the pipeline due to heat transfer from the soil, leading to an increase in oil viscosity and an increase in hydraulic resistance.The dependence of the hydraulic resistance of the pipeline on the parameters of oil pumping is determined by solving the inverse problem. The inverse problem statement consists of a system of equations of laws of conservation of momentum, mass, energy and hydraulic resistance in the form of Altshul with unknown coefficients. The system of partial differential equations of hyperbolic type for speed and pressure is solved by the numerical method of characteristics, and the heat transfer equations by the iterative method of running counting.

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