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Estimating the Extreme Financial Risk of the Kenyan Shilling Versus Us Dollar Exchange Rates
Charles Kithenge Chege,
Joseph Kyalo Mungat’u,
Oscar Ngesa
Issue:
Volume 4, Issue 6, December 2016
Pages:
249-255
Received:
1 September 2016
Accepted:
23 September 2016
Published:
14 October 2016
Abstract: In the last decade, world financial markets, including the Kenyan market have been characterized by significant instabilities. This has resulted to criticism on available risk management systems and motivated research on better methods capable of identifying rare events that have resulted in heavy consequences. With the high volatility of the Kenyan Shilling/Us dollar exchange rates, it is important to come up with a more reliable method of evaluating the financial risk associated with such financial data. In the recent past, extensive research has been carried out to analyze extreme variations that financial markets are subject to, mostly because of currency crises, stock market crashes and large credit defaults. We considered the behavior of the tails of financial series. More specially was focus on the use of extreme value theory to assess tail-related risk; we thus aim at providing a modeling tool for modern risk management. Extreme Value Theory provides a theoretical foundation on which we can build statistical models describing extreme events. This will help in predictability of such future rare events.
Abstract: In the last decade, world financial markets, including the Kenyan market have been characterized by significant instabilities. This has resulted to criticism on available risk management systems and motivated research on better methods capable of identifying rare events that have resulted in heavy consequences. With the high volatility of the Kenya...
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Statistical Models for Count Data
Alexander Kasyoki Muoka,
Oscar Owino Ngesa,
Anthony Gichuhi Waititu
Issue:
Volume 4, Issue 6, December 2016
Pages:
256-262
Received:
13 September 2016
Accepted:
23 September 2016
Published:
15 October 2016
Abstract: Statistical analyses involving count data may take several forms depending on the context of use, that is; simple counts such as the number of plants in a particular field and categorical data in which counts represent the number of items falling in each of the several categories. The mostly adapted model for analyzing count data is the Poisson model. Other models that can be considered for modeling count data are the negative binomial and the hurdle models. It is of great importance that these models are systematically considered and compared before choosing one at the expense of others to handle count data. In real world situations count data sets may have zero counts which have an importance attached to them. In this work, statistical simulation technique was used to compare the performance of these count data models. Count data sets with different proportions of zero were simulated. Akaike Information Criterion (AIC) was used in the simulation study to compare how well several count data models fit the simulated datasets. From the results of the study it was concluded that negative binomial model fits better to over-dispersed data which has below 0.3 proportion of zeros and that hurdle model performs better in data with 0.3 and above proportion of zero.
Abstract: Statistical analyses involving count data may take several forms depending on the context of use, that is; simple counts such as the number of plants in a particular field and categorical data in which counts represent the number of items falling in each of the several categories. The mostly adapted model for analyzing count data is the Poisson mod...
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Option Pricing under Delay Geometric Brownian Motion with Regime Switching
Tianyao Fang,
Liangjian Hu,
Yun Xin
Issue:
Volume 4, Issue 6, December 2016
Pages:
263-268
Received:
18 October 2016
Published:
19 October 2016
Abstract: We investigate the option pricing problem when the price dynamics of the underlying risky assets are driven by delay geometric Brownian motions with regime switching. That is, the market interest rate, the appreciation rate and the volatility of the risky assets depend on the past stock prices and the unobservable states of the economy which are modulated by a continuous-time Markov chain. The market described by the model is incomplete, the martingale measure is not unique and the Esscher transform is employed to determine an equivalent martingale measure. We proved the model has a unique positive solution and the price of the contingent claims under the model can be computable numerically if not analytically.
Abstract: We investigate the option pricing problem when the price dynamics of the underlying risky assets are driven by delay geometric Brownian motions with regime switching. That is, the market interest rate, the appreciation rate and the volatility of the risky assets depend on the past stock prices and the unobservable states of the economy which are mo...
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The Asymptotic Analysis of the Solution of an Elasticity Theory Problem for a Transversely Isotropic Hollow Cylinder with Mixed Boundary Conditions on the Side Surface
Magomed Farman Mekhtiyev,
Nina Ilyinichna Fomina,
Nazaket Boyukaga Mammadova
Issue:
Volume 4, Issue 6, December 2016
Pages:
269-275
Received:
23 September 2016
Accepted:
7 October 2016
Published:
3 November 2016
Abstract: The problem of elasticity theory for the transversely isotropic hollow cylinder with mixed conditions on the side surface is considered in the paper. Transcendental equations are obtained regarding the eigenvalues of the problem. The roots of the characteristic equations are studied thoroughly. The study of the eigenvalues allowed to establish the essential characteristics of the stress-strain state of an anisotropic shell in comparison with isotropic shells. Homogeneous solutions were built here.
Abstract: The problem of elasticity theory for the transversely isotropic hollow cylinder with mixed conditions on the side surface is considered in the paper. Transcendental equations are obtained regarding the eigenvalues of the problem. The roots of the characteristic equations are studied thoroughly. The study of the eigenvalues allowed to establish the ...
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The Optimal Harvesting of a Stochastic Gilpin-Ayala Model Under Regime Switching
Juan Hou,
Yanqun Wang,
Zhenguo Luo
Issue:
Volume 4, Issue 6, December 2016
Pages:
276-283
Received:
30 September 2016
Accepted:
13 October 2016
Published:
7 November 2016
Abstract: In this paper, we consider a stochastic Gilpin-Ayala model under regime switching. Obtain the optimal harvesting effort and the maximum sustained yield by investigating the condition of average boundness of the system, and the ergodicity of the Markov chain. Also, through an example, we have proved our conclusion.
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Bayes Estimation of Topp-Leone Distribution Under Symmetric Entropy Loss Function Based on Lower Record Values
Issue:
Volume 4, Issue 6, December 2016
Pages:
284-288
Received:
9 October 2016
Accepted:
20 October 2016
Published:
14 November 2016
Abstract: This paper will study the estimation of parameter of Topp-Leone distribution based on lower record values. First, the minimum variance unbiased estimator and maximum likelihood estimator are obtained. Then the Bayes estimator is derived under symmetric loss function and further the empirical Bayes estimators is also obtained based on marginal probability density of record sample and maximum likelihood method. Finally, the admissibility and inadmissibility of a generally class of inverse linear estimators are also discussed.
Abstract: This paper will study the estimation of parameter of Topp-Leone distribution based on lower record values. First, the minimum variance unbiased estimator and maximum likelihood estimator are obtained. Then the Bayes estimator is derived under symmetric loss function and further the empirical Bayes estimators is also obtained based on marginal proba...
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Modeling Loan Defaults in Kenya Banks as a Rare Event Using the Generalized Extreme Value Regression Model
Stephen Muthii Wanjohi,
Anthony Gichuhi Waititu,
Anthony Kibira Wanjoya
Issue:
Volume 4, Issue 6, December 2016
Pages:
289-297
Received:
4 October 2016
Accepted:
25 October 2016
Published:
16 November 2016
Abstract: Extreme value theory is the study of extremal properties of random processes, it models and measures events that occur with little probability. The extreme value theory is a robust framework to analyze the tail behavior of distributions. It has been applied extensively in hydrology, climatology, insurance and finance industry. The information of probability of customer default is very useful while analyzing the credit risks in banks. Logistic regression model has been used extensively to model the probability of loan defaults. However, it has some limitations when it comes to modeling rare events, for example, the underestimation of the default probability which could be very risky for the bank. The second limitation/drawback is that the logit link is symmetric about 0.5, this means that the response curve п(x i) approaches one at the same rate it approaches zero. To overcome these limitations the study sought to implement regression method for binary data based on extreme value theory. The objective of the study was to model loan defaults in Kenya banks using the GEV regression model. The results of GEV were compared with the results of the logistic regression model. The study found out for rare events such as loan defaults the GEV performed better than the logistic regression model. As the percentage of defaulters in a sample became smaller the GEV model to identify defaults improves whereas the logistic regression model becomes poorer.
Abstract: Extreme value theory is the study of extremal properties of random processes, it models and measures events that occur with little probability. The extreme value theory is a robust framework to analyze the tail behavior of distributions. It has been applied extensively in hydrology, climatology, insurance and finance industry. The information of pr...
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Existence of Coupled Solutions of BVP for ϕ-Laplacian Impulsive Differential Equations
Issue:
Volume 4, Issue 6, December 2016
Pages:
298-302
Received:
4 November 2016
Accepted:
25 November 2016
Published:
14 December 2016
Abstract: In this paper, we study the existence of coupled solutions of anti-periodic boundary value problems for impulsive differential equations with ϕ-Laplacian operator. Based on a pair of coupled lower and upper solutions and appropriate Nagumo condition, we prove the existence of coupled solutions for anti-periodic impulsive differential equations boundary value problems with ϕ-Laplacian operator.
Abstract: In this paper, we study the existence of coupled solutions of anti-periodic boundary value problems for impulsive differential equations with ϕ-Laplacian operator. Based on a pair of coupled lower and upper solutions and appropriate Nagumo condition, we prove the existence of coupled solutions for anti-periodic impulsive differential equations boun...
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