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1 – 10 of 373S. 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.
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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.
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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.
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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.
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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.
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Gopal Shruthi and Murugan Suvinthra
The purpose of this paper is to study large deviations for the solution processes of a stochastic equation incorporated with the effects of nonlocal condition.
Abstract
Purpose
The purpose of this paper is to study large deviations for the solution processes of a stochastic equation incorporated with the effects of nonlocal condition.
Design/methodology/approach
A weak convergence approach is adopted to establish the Laplace principle, which is same as the large deviation principle in a Polish space. The sufficient condition for any family of solutions to satisfy the Laplace principle formulated by Budhiraja and Dupuis is used in this work.
Findings
Freidlin–Wentzell type large deviation principle holds good for the solution processes of the stochastic functional integral equation with nonlocal condition.
Originality/value
The asymptotic exponential decay rate of the solution processes of the considered equation towards its deterministic counterpart can be estimated using the established results.
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Baljinder Kour, Mustafa Inc and Ashish Arora
The purpose of this paper is to present the residual power series method for solving the space time fractional variable coefficients Ito system.
Abstract
Purpose
The purpose of this paper is to present the residual power series method for solving the space time fractional variable coefficients Ito system.
Design/methodology/approach
A weighted algorithm based on the residual power series method is used numerical solution of the space time fractional Ito system variable coefficients. The authors show that this technique yields the analytical solution of the desired problem in the form of a rapidly convergent series with easily computable components.
Findings
The authors illustrate that the proposed method produces satisfactory results with respect to the other semi analytical methods. The reliability of the method and the reduction in the size of computational domain give this method a wider applicability.
Originality/value
This research presents, for the first time, a new modification of the proposed technique for aforementioned problems and some interesting results are obtained.
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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 number…
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.
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Mehrdad Moradnezhad and Hossein Miar-Naimi
The purpose of this paper is to find a closed relation for the phase noise of LC oscillators.
Abstract
Purpose
The purpose of this paper is to find a closed relation for the phase noise of LC oscillators.
Design/methodology/approach
The governing equation of oscillators is generally a stochastic nonlinear differential equation. In this paper, a closed relation for the phase noise of LC oscillators was obtained by approximating the I–V characteristic of the oscillator with third-degree polynomials and analyzing its differential equation.
Findings
This relation expresses phase noise directly in terms of circuit parameters, including the sizes of the transistors and the bias. Next, for evaluation, the phase noise of the cross-coupled oscillator without tail current was calculated with the proposed model. In this approach, the obtained equations are expressed independently of technology by combining the obtained phase noise relation and gm/ID method.
Originality/value
A technology-independent method using the gm/ID method and the closed relationship is provided to calculate phase noise.
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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 switching…
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.
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