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1 – 10 of 335
Article
Publication date: 14 May 2020

S. Saha Ray and S. Singh

This paper aims to study fractional Brownian motion and its applications to nonlinear stochastic integral equations. Bernstein polynomials have been applied to obtain the…

Abstract

Purpose

This paper aims to study fractional Brownian motion and its applications to nonlinear stochastic integral equations. Bernstein polynomials have been applied to obtain the numerical results of the nonlinear fractional stochastic integral equations.

Design/methodology/approach

Bernstein polynomials have been used to obtain the numerical solutions of nonlinear fractional stochastic integral equations. The fractional stochastic operational matrix based on Bernstein polynomial has been used to discretize the nonlinear fractional stochastic integral equation. Convergence and error analysis of the proposed method have been discussed.

Findings

Two illustrated examples have been presented to justify the efficiency and applicability of the proposed method. The corresponding obtained numerical results have been compared with the exact solutions to establish the accuracy and efficiency of the proposed method.

Originality/value

To the best of the authors’ knowledge, nonlinear stochastic Itô–Volterra integral equation driven by fractional Brownian motion has been for the first time solved by using Bernstein polynomials. The obtained numerical results well establish the accuracy and efficiency of the proposed method.

Article
Publication date: 11 February 2021

Jayanta Kumar Dash, Sumitra Panda and Golak Bihari Panda

The authors discuss the value of portfolio and Black–Scholes (B–S)-option pricing model in fuzzy environment.

Abstract

Purpose

The authors discuss the value of portfolio and Black–Scholes (B–S)-option pricing model in fuzzy environment.

Design/methodology/approach

The B–S option pricing model (OPM) is an important role of an OPM in finance. Here, every decision is taken under uncertainty. Due to randomness or vagueness, these uncertainties may be random or fuzzy or both. As the drift µ, the degree of volatility s, interest rate r, strike price k and other parameters of the value of the portfolio V(t), market price S_0 (t) and call option C(t) are not known exactly, so they are treated as positive fuzzy number. Partial expectation of fuzzy log normal distribution is derived. Also the value of portfolio at any time t and the B–S OPM in fuzzy environment are derived. A numerical example of B–S OPM is illustrated.

Findings

First, the authors are studying some various paper and some stochastic books.

Originality/value

This is a new technique.

Article
Publication date: 11 May 2010

Calum G. Turvey

The purpose of this paper is to review the life of the famous mathematician Kiyosi Itô and discuss his influence on the study of agricultural finance and agricultural economics.

Abstract

Purpose

The purpose of this paper is to review the life of the famous mathematician Kiyosi Itô and discuss his influence on the study of agricultural finance and agricultural economics.

Design/methodology/approach

This paper is a qualitative historical review.

Findings

The paper provides a biographical stretch of Itô's life. It is shown that his influence started to infiltrate the agricultural economics profession at around 1985 and is currently a major influence of a range of economic issues from farm policy to agricultural investments.

Research limitations/implications

The biography is limited to a review of Itô's academic life and influence.

Practical implications

The paper offers a historical perspective on how probability emerged as a critical piece of the economic puzzle. For scholars and practitioners of agricultural finance, the paper provides an in depth review of how Itô processes have, and can, be used.

Originality/value

This paper provides a historical perspective on Itô that is of use to students and scholars of rural credit. This is the first “biography” of Itô to discuss his influence on agricultural finance and agricultural economics.

Details

Agricultural Finance Review, vol. 70 no. 1
Type: Research Article
ISSN: 0002-1466

Keywords

Article
Publication date: 19 December 2018

Farshid Mirzaee and Nasrin Samadyar

The purpose of this paper is to develop a new method based on operational matrices of Bernoulli wavelet for solving linear stochastic Itô-Volterra integral equations, numerically.

Abstract

Purpose

The purpose of this paper is to develop a new method based on operational matrices of Bernoulli wavelet for solving linear stochastic Itô-Volterra integral equations, numerically.

Design/methodology/approach

For this aim, Bernoulli polynomials and Bernoulli wavelet are introduced, and their properties are expressed. Then, the operational matrix and the stochastic operational matrix of integration based on Bernoulli wavelet are calculated for the first time.

Findings

By applying these matrices, the main problem would be transformed into a linear system of algebraic equations which can be solved by using a suitable numerical method. Also, a few results related to error estimate and convergence analysis of the proposed scheme are investigated.

Originality/value

Two numerical examples are included to demonstrate the accuracy and efficiency of the proposed method. All of the numerical calculation is performed on a personal computer by running some codes written in MATLAB software.

Details

Multidiscipline Modeling in Materials and Structures, vol. 15 no. 3
Type: Research Article
ISSN: 1573-6105

Keywords

Article
Publication date: 3 July 2017

Edita Kolarova and Lubomir Brancik

The purpose of this paper is to determine confidence intervals for the stochastic solutions in RLCG cells with a potential source influenced by coloured noise.

Abstract

Purpose

The purpose of this paper is to determine confidence intervals for the stochastic solutions in RLCG cells with a potential source influenced by coloured noise.

Design/methodology/approach

The deterministic model of the basic RLCG cell leads to an ordinary differential equation. In this paper, a stochastic model is formulated and the corresponding stochastic differential equation is analysed using the Itô stochastic calculus.

Findings

Equations for the first and the second moment of the stochastic solution of the coloured noise-affected RLCG cell are obtained, and the corresponding confidence intervals are determined. The moment equations lead to ordinary differential equations, which are solved numerically by an implicit Euler scheme, which turns out to be very effective. For comparison, the confidence intervals are computed statistically by an implementation of the Euler scheme using stochastic differential equations.

Practical implications/implications

The theoretical results are illustrated by examples. Numerical simulations in the examples are carried out using Matlab. A possible generalization for transmission line models is indicated.

Originality/value

The Itô-type stochastic differential equation describing the coloured noise RLCG cell is formulated, and equations for the respective moments are derived. Owing to this original approach, the confidence intervals can be found more effectively by solving a system of ordinary differential equations rather than by using statistical methods.

Details

COMPEL - The international journal for computation and mathematics in electrical and electronic engineering, vol. 36 no. 4
Type: Research Article
ISSN: 0332-1649

Keywords

Article
Publication date: 15 August 2019

Stan Hurn, Kenneth A. Lindsay and Lina Xu

The purpose of this paper is to revisit the numerical solutions of stochastic differential equations (SDEs). An important drawback when integrating SDEs numerically is the…

Abstract

Purpose

The purpose of this paper is to revisit the numerical solutions of stochastic differential equations (SDEs). An important drawback when integrating SDEs numerically is the number of steps required to attain acceptable accuracy of convergence to the true solution.

Design/methodology/approach

This paper develops a bias reducing method based loosely on extrapolation.

Findings

The method is seen to perform acceptably well and for realistic steps sizes provides improved accuracy at no significant additional computational cost. In addition, the optimal step size of the bias reduction methods is shown to be consistent with theoretical analysis.

Originality/value

Overall, there is evidence to suggest that the proposed method is a viable, easy to implement competitor for other commonly used numerical schemes.

Details

China Finance Review International, vol. 9 no. 3
Type: Research Article
ISSN: 2044-1398

Keywords

Article
Publication date: 27 September 2011

Fangcheng Hao and Hailiang Yang

The purpose of this paper is to provide a scenario‐based risk measure for a portfolio of European‐style derivative securities over a fixed time horizon under the regime…

Abstract

Purpose

The purpose of this paper is to provide a scenario‐based risk measure for a portfolio of European‐style derivative securities over a fixed time horizon under the regime switching Black‐Scholes economy.

Design/methodology/approach

The risk measure is constructed by using the risk‐neutral probability, the physical probability and a family of subjective probability measures. The subjective probabilities can be interpreted as risk managers or regulators' risk preferences and/or subjective beliefs.

Findings

The authors provide closed form expressions for the European option and barrier option.

Research limitations/implications

The results are difficult to apply to a portfolio with many different kinds of options.

Practical implications

The results provide some insights on risk management of portfolios with derivatives.

Originality/value

The paper presents a scenario‐based risk measure for a portfolio of European‐style derivative securities over a fixed time horizon under the regime switching Black‐Scholes economy. Risk management is the most important task for almost all financial industries, although it cannot be claimed that the method and results of this paper solve the problem, it is believed to provide some insights to the problem, albeit theoretical. For vanilla European options and barrier options, the authors obtained a closed form expression for the risk measure. The idea of this paper can be applied to some other exotic options. For portfolios containing different kinds of derivatives, the results of this paper provide some guideline and insights.

Details

Managerial Finance, vol. 37 no. 11
Type: Research Article
ISSN: 0307-4358

Keywords

Article
Publication date: 1 October 2006

Y. Tamura, S. Yamada and M. Kimura

The aim of this paper is to propose a software reliability growth model based on stochastic differential equations for the integration testing phase of distributed…

Abstract

Purpose

The aim of this paper is to propose a software reliability growth model based on stochastic differential equations for the integration testing phase of distributed development environment.

Design/methodology/approach

A client/server system (CSS), which is a new development method, has come into existence as a result of the progress of networking technology by UNIX systems. On the other hand, the effective testing method for distributed development environment has only a few presented. The method of software reliability assessment considering the interaction among software components in a distributed one is discussed.

Findings

Conventional software reliability growth models for system testing phase in distributed development environment have included many unknown parameters. Especially, the effective estimation method in terms of these unknown parameters, which means the proportion of the total testing‐load for the software component, has never been presented. This software reliability growth model can be easily applied in distributed software development, because the model has a simple structure.

Practical implications

This model is very useful for software developers in terms of practical reliability assessment in the actual distributed development environment.

Originality/value

The method of software reliability assessment considering the interaction among software components in distributed development environment is proposed. Additionally, several numerical examples for the actual data are presented.

Details

Journal of Quality in Maintenance Engineering, vol. 12 no. 4
Type: Research Article
ISSN: 1355-2511

Keywords

Article
Publication date: 9 April 2021

Jiao Wang

This paper aims to propose an efficient and convenient numerical algorithm for two-dimensional nonlinear Volterra-Fredholm integral equations and fractional…

Abstract

Purpose

This paper aims to propose an efficient and convenient numerical algorithm for two-dimensional nonlinear Volterra-Fredholm integral equations and fractional integro-differential equations (of Hammerstein and mixed types).

Design/methodology/approach

The main idea of the presented algorithm is to combine Bernoulli polynomials approximation with Caputo fractional derivative and numerical integral transformation to reduce the studied two-dimensional nonlinear Volterra-Fredholm integral equations and fractional integro-differential equations to easily solved algebraic equations.

Findings

Without considering the integral operational matrix, this algorithm will adopt straightforward discrete data integral transformation, which can do good work to less computation and high precision. Besides, combining the convenient fractional differential operator of Bernoulli basis polynomials with the least-squares method, numerical solutions of the studied equations can be obtained quickly. Illustrative examples are given to show that the proposed technique has better precision than other numerical methods.

Originality/value

The proposed algorithm is efficient for the considered two-dimensional nonlinear Volterra-Fredholm integral equations and fractional integro-differential equations. As its convenience, the computation of numerical solutions is time-saving and more accurate.

Article
Publication date: 1 October 2006

Truc Le and Eckhard Platen

This paper aims to construct and compare various total‐return world stock indices based on daily data.

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Abstract

Purpose

This paper aims to construct and compare various total‐return world stock indices based on daily data.

Design/methodology/approach

Because of diversification, these indices are noticeably similar. A diversification theorem identifies any diversified portfolio as a proxy for the growth optimal portfolio.

Findings

The paper constructs a diversified world stock index that outperforms a number of other indices and argues that it is a good proxy for the growth optimal portfolio.

Originality/value

The diversified world stock index has applications to derivative pricing and investment management.

Details

The Journal of Risk Finance, vol. 7 no. 5
Type: Research Article
ISSN: 1526-5943

Keywords

1 – 10 of 335