scholarly journals Comparative study of the behavior of the effective boundary of minimal risk portfolio in the conditions of hybrid uncertainty, depending on the restrictions on the profitability of the portfolio

2021 ◽  
pp. 58-69
Author(s):  
Александр Васильевич Язенин ◽  
Илья Сергеевич Солдатенко
Keyword(s):  
Comparative Study ◽  
Numerical Experiments ◽  
Minimal Risk ◽  
Two Dimensional ◽  
Probability Level ◽  
Expected Return ◽  
Minimum Risk ◽  
Effective Boundary ◽  
Hybrid Uncertainty ◽  
Theoretical Results

В работе проведены исследования эффективной границы портфеля минимального риска в условиях гибридной неопределенности. Для случая двумерного портфеля при ограничении на ожидаемую доходность портфеля и ограничении по возможности/необходимости и вероятности на доходность портфеля в зависимости от уровня вероятности построены квазиэффективные границы портфеля. Результаты численных экспериментов согласуются с ранее полученными авторами теоретическими результатами. The paper studies the effective boundary of the minimum risk portfolio in the conditions of hybrid uncertainty. For the case of a two-dimensional portfolio, with a restriction on the expected return of the portfolio and a restriction on possibility/necessity and probability on the return of the portfolio, quasi-effective portfolio boundaries are constructed depending on the probability level. The results of numerical experiments are consistent with the theoretical results previously obtained by the authors.

scholarly journals On one problem of portfolio analysis under soft constraints

2020 ◽  
pp. 64-76
Author(s):  
Илья Сергеевич Солдатенко ◽  
Александр Васильевич Язенин
Keyword(s):  
Binary Relation ◽  
Portfolio Analysis ◽  
Minimal Risk ◽  
Soft Constraints ◽  
Investment Portfolio ◽  
Expected Return ◽  
Hybrid Uncertainty

Разработана и исследована модель портфеля минимального риска в условиях гибридной неопределенности возможностно-вероятностного типа, основанная на принципе ожидаемой возможности. Особенностью рассматриваемой модели является то, что «мягкость» ограничения на уровень ожидаемой доходности моделируется путем замены четкого ограничения возможностным бинарным отношением. На модельном примере показано, как мягкость ограничения влияет на множество квазиэффективных оценок инвестиционного портфеля. A model of a minimal risk portfolio under conditions of hybrid uncertainty of the possibility-probability type based on the principle of expected possibility has been developed and studied. The peculiarity of this model is that the "softness" of the restriction on the level of expected return is modeled by replacing a clear restriction with a possibilistic binary relation. The model example shows how the softness of the constraint affects a set of quasi-effective estimates of an investment portfolio.

scholarly journals Quadrature Rules and Iterative Method for Numerical Solution of Two-Dimensional Fuzzy Integral Equations

2014 ◽  
Vol 2014 ◽  
pp. 1-18 ◽  
Author(s):  
S. M. Sadatrasoul ◽  
R. Ezzati
Keyword(s):  
Integral Equations ◽  
Iterative Procedure ◽  
Numerical Experiments ◽  
Quadrature Rules ◽  
Fredholm Integral Equations ◽  
Fuzzy Integral ◽  
Two Dimensional ◽  
Henstock Integral ◽  
Uniform Modulus Of Continuity ◽  
Theoretical Results

We introduce some generalized quadrature rules to approximate two-dimensional, Henstock integral of fuzzy-number-valued functions. We also give error bounds for mappings of bounded variation in terms of uniform modulus of continuity. Moreover, we propose an iterative procedure based on quadrature formula to solve two-dimensional linear fuzzy Fredholm integral equations of the second kind (2DFFLIE2), and we present the error estimation of the proposed method. Finally, some numerical experiments confirm the theoretical results and illustrate the accuracy of the method.

A NONCONFORMING PENALTY METHOD FOR A TWO-DIMENSIONAL CURL–CURL PROBLEM

2009 ◽  
Vol 19 (04) ◽  
pp. 651-668 ◽  
Author(s):  
SUSANNE C. BRENNER ◽  
FENGYAN LI ◽  
LI-YENG SUNG
Keyword(s):  
Numerical Experiments ◽  
Vector Fields ◽  
Convergence Rates ◽  
Two Dimensional ◽  
Weakly Continuous ◽  
Graded Meshes ◽  
Optimal Convergence Rates ◽  
Maxwell Eigenvalues ◽  
Theoretical Results ◽  
Convergence Of The Scheme

A nonconforming finite element method for a two-dimensional curl–curl problem is studied in this paper. It uses weakly continuous P1 vector fields and penalizes the local divergence. Two consistency terms involving the jumps of the vector fields across element boundaries are also included to ensure the convergence of the scheme. Optimal convergence rates (up to an arbitrary positive ∊) in both the energy norm and the L2 norm are established on graded meshes. This scheme can also be used in the computation of Maxwell eigenvalues without generating spurious eigenmodes. The theoretical results are confirmed by numerical experiments.

scholarly journals On the Application of the Generalized Means to Construct Multiresolution Schemes Satisfying Certain Inequalities Proving Stability

Mathematics ◽  
2021 ◽  
Vol 9 (5) ◽  
pp. 533
Author(s):  
Sergio Amat ◽  
Alberto Magreñan ◽  
Juan Ruiz ◽  
Juan Carlos Trillo ◽  
Dionisio F. Yañez
Keyword(s):  
Numerical Experiments ◽  
Order Of Approximation ◽  
Two Dimensional ◽  
Nonlinear Subdivision ◽  
Proper Definition ◽  
The Stability ◽  
Definition Of ◽  
Stability Issues ◽  
Multiresolution Schemes ◽  
Theoretical Results

Multiresolution representations of data are known to be powerful tools in data analysis and processing, and they are particularly interesting for data compression. In order to obtain a proper definition of the edges, a good option is to use nonlinear reconstructions. These nonlinear reconstruction are the heart of the prediction processes which appear in the definition of the nonlinear subdivision and multiresolution schemes. We define and study some nonlinear reconstructions based on the use of nonlinear means, more in concrete the so-called Generalized means. These means have two interesting properties that will allow us to get associated reconstruction operators adapted to the presence of discontinuities, and having the maximum possible order of approximation in smooth areas. Once we have these nonlinear reconstruction operators defined, we can build the related nonlinear subdivision and multiresolution schemes and prove more accurate inequalities regarding the contractivity of the scheme for the first differences and in turn the results about stability. In this paper, we also define a new nonlinear two-dimensional multiresolution scheme as non-separable, i.e., not based on tensor product. We then present the study of the stability issues for the scheme and numerical experiments reinforcing the proven theoretical results and showing the usefulness of the algorithm.

scholarly journals OPTIMAL PORTFOLIO ANALYSIS OF IDX-30 AND LQ-45 PORTFOLIO WITH THE CAPM METHOD OF THE INDONESIA STOCK EXCHANGE

2020 ◽  
Vol 1 (2) ◽  
pp. 132-141
Author(s):  
Nur Sarva Jayana ◽  
Pardomuan Sihombing
Keyword(s):  
Stock Exchange ◽  
Sampling Technique ◽  
Optimal Portfolio ◽  
Portfolio Performance ◽  
Minimal Risk ◽  
Microsoft Excel ◽  
Expected Return ◽  
Minimum Risk ◽  
Sample Data ◽  
Investment Returns

The research objective of this portfolio is to analyze the optimal portfolio IDX-30 and its portfolio of LQ-45 with CAPM method in IDX. This research uses descriptive quantitative method. IDX-30 and LQ-45 in the Stock Exchange of the period January 2013 - December 2018 the population in the study. A Purposive sampling technique used in determining the sample. Data analysis using Microsoft Excel, from this research are, a). Based on the results of the expected return and risk of IDX-30 and LQ-45, which can be seen from an analysis of individual stocks with a CAPM portfolio. Then the chosen CAPM portfolio, because it produces a good return and minimal risk. And the highest shares of IDX-30 and LQ-45 are TLKM. with the IDX-P13 return result of 6.5809 and a risk of 7.14%. and LQ-45 P20 return of 6.5764 with a risk of 7.89%.b). Optimal portfolios formed using CAPM provide better investment returns than individual shares, because CAPM offers a higher expected return and minimum risk than individual shares. While the optimal portfolio performance of IDX-30 shares evaluated using CAPM is better than the optimal portfolio performance of LQ-45 shares.

scholarly journals An Intuitive Introduction to Fractional and Rough Volatilities

Mathematics ◽  
2021 ◽  
Vol 9 (9) ◽  
pp. 994
Author(s):  
Elisa Alòs ◽  
Jorge A. León
Keyword(s):  
Malliavin Calculus ◽  
Numerical Experiments ◽  
Implied Volatility ◽  
Natural Approach ◽  
Volatility Models ◽  
Implied Volatility Surface ◽  
Short Memory ◽  
White Type ◽  
Volatility Surface ◽  
Theoretical Results

Here, we review some results of fractional volatility models, where the volatility is driven by fractional Brownian motion (fBm). In these models, the future average volatility is not a process adapted to the underlying filtration, and fBm is not a semimartingale in general. So, we cannot use the classical Itô’s calculus to explain how the memory properties of fBm allow us to describe some empirical findings of the implied volatility surface through Hull and White type formulas. Thus, Malliavin calculus provides a natural approach to deal with the implied volatility without assuming any particular structure of the volatility. The aim of this paper is to provides the basic tools of Malliavin calculus for the study of fractional volatility models. That is, we explain how the long and short memory of fBm improves the description of the implied volatility. In particular, we consider in detail a model that combines the long and short memory properties of fBm as an example of the approach introduced in this paper. The theoretical results are tested with numerical experiments.

Computational models of filtration gas combustion

2017 ◽  
Vol 32 (2) ◽  
Author(s):  
Yuri M. Laevsky ◽  
Tatyana A. Nosova
Keyword(s):  
Heat Flow ◽  
Numerical Experiments ◽  
Computational Models ◽  
Two Dimensional ◽  
Multidimensional Model ◽  
Gas Combustion ◽  
Total Enthalpy ◽  
Diffusive Flow ◽  
Temperature Heat ◽  
The One

AbstractA multidimensional model of filtration gas combustion is presented. The model is based on the system of conservation laws of ‘temperature – heat flow’, ‘mass–diffusive flow’ types with introducing the concept of total enthalpy flow. Results of numerical experiments are presented for the one- and two-dimensional problems for different conditions and parameters.

Comparative study of dissipation modeling in two-dimensional MHD turbulence

1990 ◽  
Vol 2 (1) ◽  
pp. 47-60 ◽  
Author(s):  
T. Passot ◽  
H. Politano ◽  
A. Pouquet ◽  
P. L. Sulem
Keyword(s):  
Comparative Study ◽  
Two Dimensional ◽  
Mhd Turbulence

The Effect of Froude Number on Entrainment in Two-Dimensional Line Plumes

1981 ◽  
Vol 103 (3) ◽  
pp. 471-477 ◽  
Author(s):  
W. F. Phillips
Keyword(s):  
Froude Number ◽  
Large Distance ◽  
Universal Constant ◽  
Temperature Profiles ◽  
Two Dimensional ◽  
Development Length ◽  
High Discharge ◽  
Entrainment Coefficient ◽  
Theoretical Results

Theoretical results are presented which predict the entrainment coefficient in a forced plume as a function of the local Froude number. The model does not require any external specification of the velocity and temperature profiles. The Froude number for any plume, in a motionless isothermal ambient, approaches a universal constant, at a large distance above the source. However, it is shown here that the development length for the Froude number, in plumes with high discharge Froude number, is of the order of a few hundred times the discharge width.

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