Pub Date : 2023-01-01DOI: 10.3844/jmssp.2023.13.19
S. Sani, Siphelele Lushaba
: In this study, Ito form for normal bonds trading where maturity periods cross over to COVID-19 pandemic period is presented. It is shown that normal bonds in this period experience path reversals respective to their canonical paths. The criterion used in arriving at this striking result is also presented. As a key recommendation, it is necessary that bondholders enact flexible pricing laws that strengthen the issuer to continue trading in the present COVID-19 pandemic time through the reverse path identified in this study.
{"title":"Stochastic Model for Pricing Normal Bonds when Maturity Periods Cross Over to Pandemic Period","authors":"S. Sani, Siphelele Lushaba","doi":"10.3844/jmssp.2023.13.19","DOIUrl":"https://doi.org/10.3844/jmssp.2023.13.19","url":null,"abstract":": In this study, Ito form for normal bonds trading where maturity periods cross over to COVID-19 pandemic period is presented. It is shown that normal bonds in this period experience path reversals respective to their canonical paths. The criterion used in arriving at this striking result is also presented. As a key recommendation, it is necessary that bondholders enact flexible pricing laws that strengthen the issuer to continue trading in the present COVID-19 pandemic time through the reverse path identified in this study.","PeriodicalId":41981,"journal":{"name":"Jordan Journal of Mathematics and Statistics","volume":"5 1","pages":""},"PeriodicalIF":0.3,"publicationDate":"2023-01-01","publicationTypes":"Journal Article","fieldsOfStudy":null,"isOpenAccess":false,"openAccessPdf":"","citationCount":null,"resultStr":null,"platform":"Semanticscholar","paperid":"79778133","PeriodicalName":null,"FirstCategoryId":null,"ListUrlMain":null,"RegionNum":0,"RegionCategory":"","ArticlePicture":[],"TitleCN":null,"AbstractTextCN":null,"PMCID":"","EPubDate":null,"PubModel":null,"JCR":null,"JCRName":null,"Score":null,"Total":0}
: Recently, it has been reported that the hypothesis proposed by the classical black Scholes model to price multivariate options in finance were unrealistic, as such, several other methods have been introduced over the last decades including the copulas methods which uses copulas functions to model the dependence structure of underlying assets. However, the previous work did not take into account the use of mixed copulas to assess the underlying assets' dependence structure. The approach we propose consists of selecting the appropriate mixed copula’s structure which captures as much information as possible about the asset’s dependence structure and apply a copulas-based martingale strategy to price multivariate equity options using monte Carlo simulation. A mixture of normal distributions estimated with the standard EM algorithm is also considered for modeling the marginal distribution of financial asset returns. Moreover, the Monte Carlo simulation is performed to compute the values of exotic and up and out barrier options such as worst of, spread, and rainbow options, which shows that the clayton gumble and clayton gaussian have relatively large values for all the options. Our results further indicate that the mixed copula-based approach can be used efficiently to capture heterogeneous dependence structure existing in multivariate assets, price exotic options and generalize the existing results.
{"title":"Multivariate Option Pricing with Gaussian Mixture Distributions and Mixed Copulas","authors":"J. H. Claver, Tatanfack Emerson, Shu Felix","doi":"10.3844/jmssp.2023.1.12","DOIUrl":"https://doi.org/10.3844/jmssp.2023.1.12","url":null,"abstract":": Recently, it has been reported that the hypothesis proposed by the classical black Scholes model to price multivariate options in finance were unrealistic, as such, several other methods have been introduced over the last decades including the copulas methods which uses copulas functions to model the dependence structure of underlying assets. However, the previous work did not take into account the use of mixed copulas to assess the underlying assets' dependence structure. The approach we propose consists of selecting the appropriate mixed copula’s structure which captures as much information as possible about the asset’s dependence structure and apply a copulas-based martingale strategy to price multivariate equity options using monte Carlo simulation. A mixture of normal distributions estimated with the standard EM algorithm is also considered for modeling the marginal distribution of financial asset returns. Moreover, the Monte Carlo simulation is performed to compute the values of exotic and up and out barrier options such as worst of, spread, and rainbow options, which shows that the clayton gumble and clayton gaussian have relatively large values for all the options. Our results further indicate that the mixed copula-based approach can be used efficiently to capture heterogeneous dependence structure existing in multivariate assets, price exotic options and generalize the existing results.","PeriodicalId":41981,"journal":{"name":"Jordan Journal of Mathematics and Statistics","volume":"67 1","pages":""},"PeriodicalIF":0.3,"publicationDate":"2023-01-01","publicationTypes":"Journal Article","fieldsOfStudy":null,"isOpenAccess":false,"openAccessPdf":"","citationCount":null,"resultStr":null,"platform":"Semanticscholar","paperid":"77714582","PeriodicalName":null,"FirstCategoryId":null,"ListUrlMain":null,"RegionNum":0,"RegionCategory":"","ArticlePicture":[],"TitleCN":null,"AbstractTextCN":null,"PMCID":"","EPubDate":null,"PubModel":null,"JCR":null,"JCRName":null,"Score":null,"Total":0}
Pub Date : 2022-01-01DOI: 10.3844/jmssp.2022.78.86
M. Yaremenko
: In this article, the spectral theory is considered, we study the spectral families and their correspondence to the operators on the reflexive Banach spaces; assume A is a well-bounded operator on reflexive Lebesgue spaces then the operator A is a scalar type spectral operator. The main goals are to obtain the characterization of the well-bounded operators in the terms of the associated spectral family in the topology of dual pairing and to construct the continuous functional calculus for well-bounded operators on the Lebesgue space.
{"title":"Measurable Functional Calculi and Spectral Theory","authors":"M. Yaremenko","doi":"10.3844/jmssp.2022.78.86","DOIUrl":"https://doi.org/10.3844/jmssp.2022.78.86","url":null,"abstract":": In this article, the spectral theory is considered, we study the spectral families and their correspondence to the operators on the reflexive Banach spaces; assume A is a well-bounded operator on reflexive Lebesgue spaces then the operator A is a scalar type spectral operator. The main goals are to obtain the characterization of the well-bounded operators in the terms of the associated spectral family in the topology of dual pairing and to construct the continuous functional calculus for well-bounded operators on the Lebesgue space.","PeriodicalId":41981,"journal":{"name":"Jordan Journal of Mathematics and Statistics","volume":"19 1","pages":""},"PeriodicalIF":0.3,"publicationDate":"2022-01-01","publicationTypes":"Journal Article","fieldsOfStudy":null,"isOpenAccess":false,"openAccessPdf":"","citationCount":null,"resultStr":null,"platform":"Semanticscholar","paperid":"73375300","PeriodicalName":null,"FirstCategoryId":null,"ListUrlMain":null,"RegionNum":0,"RegionCategory":"","ArticlePicture":[],"TitleCN":null,"AbstractTextCN":null,"PMCID":"","EPubDate":null,"PubModel":null,"JCR":null,"JCRName":null,"Score":null,"Total":0}
Pub Date : 2022-01-01DOI: 10.3844/jmssp.2022.49.64
J. Tsetimi, M. I. Ossaiugbo, A. Atonuje
Corresponding Author: Jonathan Tsetimi Department of Mathematics, Faculty of Science, Delta State University, Abraka, Nigeria Email: tsetimi@yahoo.com Abstract: The dreaded COVID-19 is a communicable respiratory disease caused by a new strain of coronavirus that causes illness in humans. A study of the transmission dynamics of the disease is essential in the control and elimination of the disease. In this research work, we made some assumptions and employed a deterministic SEIR model in the study of the transmission dynamics of the novel coronavirus disease. A mathematical analysis is performed on the model. This analysis includes the positivity of solutions of the model, boundedness of solution, equilibrium points, basic reproduction number, stability and sensitivity analysis. The effects of some sensitive parameters of the basic reproduction number of the COVID-19 disease are made visible in the numerical solutions of the disease model. These simulations which can be employed as a guide in the control and elimination of the disease shows that individual’s compliance to government’s laws on the use of facemask and social distancing is a major successful tool to be positively embraced in the fight against this human enemy.
{"title":"A Mathematical Model and Analysis for the COVID-19 Infection","authors":"J. Tsetimi, M. I. Ossaiugbo, A. Atonuje","doi":"10.3844/jmssp.2022.49.64","DOIUrl":"https://doi.org/10.3844/jmssp.2022.49.64","url":null,"abstract":"Corresponding Author: Jonathan Tsetimi Department of Mathematics, Faculty of Science, Delta State University, Abraka, Nigeria Email: tsetimi@yahoo.com Abstract: The dreaded COVID-19 is a communicable respiratory disease caused by a new strain of coronavirus that causes illness in humans. A study of the transmission dynamics of the disease is essential in the control and elimination of the disease. In this research work, we made some assumptions and employed a deterministic SEIR model in the study of the transmission dynamics of the novel coronavirus disease. A mathematical analysis is performed on the model. This analysis includes the positivity of solutions of the model, boundedness of solution, equilibrium points, basic reproduction number, stability and sensitivity analysis. The effects of some sensitive parameters of the basic reproduction number of the COVID-19 disease are made visible in the numerical solutions of the disease model. These simulations which can be employed as a guide in the control and elimination of the disease shows that individual’s compliance to government’s laws on the use of facemask and social distancing is a major successful tool to be positively embraced in the fight against this human enemy.","PeriodicalId":41981,"journal":{"name":"Jordan Journal of Mathematics and Statistics","volume":"25 1","pages":""},"PeriodicalIF":0.3,"publicationDate":"2022-01-01","publicationTypes":"Journal Article","fieldsOfStudy":null,"isOpenAccess":false,"openAccessPdf":"","citationCount":null,"resultStr":null,"platform":"Semanticscholar","paperid":"84705900","PeriodicalName":null,"FirstCategoryId":null,"ListUrlMain":null,"RegionNum":0,"RegionCategory":"","ArticlePicture":[],"TitleCN":null,"AbstractTextCN":null,"PMCID":"","EPubDate":null,"PubModel":null,"JCR":null,"JCRName":null,"Score":null,"Total":0}
Pub Date : 2022-01-01DOI: 10.3844/jmssp.2022.106.114
Orlando M. Patricio, R. Goonatilake, F. Quintana, Hong-wei Wang, Francisco J. Cervantes-Gonzalez
: This study aimed to determine the probability of fatty liver, hepatomegaly, and liver size ≥2SD with age in each category of BMI percentile. It also aimed to investigate the relationship between GFR, BMI percentile, liver size, Blood Pressure (BP), and right kidney volume among overweight and obese boys and girls and to identify the predictors of GFR. 763 records of boys and girls visiting a pediatric clinic in South Texas from 2003 to 2018 were assessed. Statistical analyses such as linear regression, binary logistic regression, cubic estimation, path analysis, and factor analysis were performed. It was found that among all the BMI percentile categories, boys have larger liver sizes than girls. Obese boys and girls have the largest liver size than overweight boys and girls followed by normal (robust) and underweight (slim) boys and girls. As the BMI percentile increases, the probability of fatty liver, hepatomegaly, and liver size ≥2SD increases. As the BMI percentile increases, decreased kidney function prevalence increases in the young Mexican American population. Decreased kidney function is also affected by liver enlargement and increased systolic blood pressure. Obese boys' and girls' kidney function start to drop at age 7.755 while overweight boys' and girls' start to fall at age 9.185. The exponential trends in the probabilities between liver size and age indicate that overweight and obese boys and girls are at higher risk for fatty and enlarged liver. Overweight and obese boys and girls have reduced kidney function as indicated by their decreasing GFR. High BMI percentile, increased liver size, and increased systolic blood pressure are precursors (predictors) to decreased kidney function.
{"title":"Predictive Analysis of BMI and Liver Size on Kidney Function in Young Mexican American Population","authors":"Orlando M. Patricio, R. Goonatilake, F. Quintana, Hong-wei Wang, Francisco J. Cervantes-Gonzalez","doi":"10.3844/jmssp.2022.106.114","DOIUrl":"https://doi.org/10.3844/jmssp.2022.106.114","url":null,"abstract":": This study aimed to determine the probability of fatty liver, hepatomegaly, and liver size ≥2SD with age in each category of BMI percentile. It also aimed to investigate the relationship between GFR, BMI percentile, liver size, Blood Pressure (BP), and right kidney volume among overweight and obese boys and girls and to identify the predictors of GFR. 763 records of boys and girls visiting a pediatric clinic in South Texas from 2003 to 2018 were assessed. Statistical analyses such as linear regression, binary logistic regression, cubic estimation, path analysis, and factor analysis were performed. It was found that among all the BMI percentile categories, boys have larger liver sizes than girls. Obese boys and girls have the largest liver size than overweight boys and girls followed by normal (robust) and underweight (slim) boys and girls. As the BMI percentile increases, the probability of fatty liver, hepatomegaly, and liver size ≥2SD increases. As the BMI percentile increases, decreased kidney function prevalence increases in the young Mexican American population. Decreased kidney function is also affected by liver enlargement and increased systolic blood pressure. Obese boys' and girls' kidney function start to drop at age 7.755 while overweight boys' and girls' start to fall at age 9.185. The exponential trends in the probabilities between liver size and age indicate that overweight and obese boys and girls are at higher risk for fatty and enlarged liver. Overweight and obese boys and girls have reduced kidney function as indicated by their decreasing GFR. High BMI percentile, increased liver size, and increased systolic blood pressure are precursors (predictors) to decreased kidney function.","PeriodicalId":41981,"journal":{"name":"Jordan Journal of Mathematics and Statistics","volume":"1 1","pages":""},"PeriodicalIF":0.3,"publicationDate":"2022-01-01","publicationTypes":"Journal Article","fieldsOfStudy":null,"isOpenAccess":false,"openAccessPdf":"","citationCount":null,"resultStr":null,"platform":"Semanticscholar","paperid":"89630338","PeriodicalName":null,"FirstCategoryId":null,"ListUrlMain":null,"RegionNum":0,"RegionCategory":"","ArticlePicture":[],"TitleCN":null,"AbstractTextCN":null,"PMCID":"","EPubDate":null,"PubModel":null,"JCR":null,"JCRName":null,"Score":null,"Total":0}
Pub Date : 2022-01-01DOI: 10.3844/jmssp.2022.176.195
B. Bassey, A. O. Henry
: From the studies of HIV/AIDS transmission and treatment dynamics using mathematical modeling, literature reviews have shown that attention had not been given to the behavioral attitude of screen-aware infectives not ready to receive treatment, HIV-aware infectives that initiated treatment but truncated only to resume treatment later (therapy abuse) and those on consistent treatment protocols. Moreso, following the non-outright eradication of the deadly HI-virus, recommendations have been geared towards exploring optimal control theory for the maximization of healthy uninfected CD4 + T-cells. Therefore, this present investigation seeks and formulated an optimal control 6-Dimensional deterministic mathematical dynamic model, which accounted for the Role of Antiretroviral Therapy (ART) abuse in the treatment dynamics of the HIV/AIDS epidemic. The materials and methods for this model are constituted by a set of 6-Dimensional varying subpopulations interacting with concentrated HI-viral load. Interactions are investigated using bilinear control functions (condom use and ART) with empirically generated data. The model assumed a deterministic approach and was formulated using the fundamental theory of differential equations. Theoretical optimal predictions explored classical numerical methods with optimal control techniques (Pontryagin's maximum principle in conjunction with Hessian matrix) as a basis. Numerical simulations were conducted using in-built Runge-Kutta of the order of precision 4 in a Mathcad surface. Following the derived model for both off-optimal control and onset-optimal control functions and model optimal control pair as well as model optimality system, results of simulations indicated that at off-optimal control function, near zero population extinction was observed. From the application of optimal control functions under optimal control techniques, there exists tremendous rejuvenation of susceptible populations vindicated by a reduction in the rate of ART abuse under a minimal proportion of bilinear control functions. The study concluded that adopting optimal control techniques for the investigation of the role of ART abuse in HIV/AIDS treatment yield highly significant recovery of healthy CD4 + T-Cells at minimal systemic cost when compared with off-optimal control outcome. Therefore, the study not only affirmed the vital concept of optimal control strategy but also, instituted the viability of the model. Thus, this model can be extensively used in Bio-system and applied mathematics.
{"title":"Optimal Control Techniques for the Role of Antiretroviral Therapy (ART) Abuse in HIV/AIDS Treatment Dynamics","authors":"B. Bassey, A. O. Henry","doi":"10.3844/jmssp.2022.176.195","DOIUrl":"https://doi.org/10.3844/jmssp.2022.176.195","url":null,"abstract":": From the studies of HIV/AIDS transmission and treatment dynamics using mathematical modeling, literature reviews have shown that attention had not been given to the behavioral attitude of screen-aware infectives not ready to receive treatment, HIV-aware infectives that initiated treatment but truncated only to resume treatment later (therapy abuse) and those on consistent treatment protocols. Moreso, following the non-outright eradication of the deadly HI-virus, recommendations have been geared towards exploring optimal control theory for the maximization of healthy uninfected CD4 + T-cells. Therefore, this present investigation seeks and formulated an optimal control 6-Dimensional deterministic mathematical dynamic model, which accounted for the Role of Antiretroviral Therapy (ART) abuse in the treatment dynamics of the HIV/AIDS epidemic. The materials and methods for this model are constituted by a set of 6-Dimensional varying subpopulations interacting with concentrated HI-viral load. Interactions are investigated using bilinear control functions (condom use and ART) with empirically generated data. The model assumed a deterministic approach and was formulated using the fundamental theory of differential equations. Theoretical optimal predictions explored classical numerical methods with optimal control techniques (Pontryagin's maximum principle in conjunction with Hessian matrix) as a basis. Numerical simulations were conducted using in-built Runge-Kutta of the order of precision 4 in a Mathcad surface. Following the derived model for both off-optimal control and onset-optimal control functions and model optimal control pair as well as model optimality system, results of simulations indicated that at off-optimal control function, near zero population extinction was observed. From the application of optimal control functions under optimal control techniques, there exists tremendous rejuvenation of susceptible populations vindicated by a reduction in the rate of ART abuse under a minimal proportion of bilinear control functions. The study concluded that adopting optimal control techniques for the investigation of the role of ART abuse in HIV/AIDS treatment yield highly significant recovery of healthy CD4 + T-Cells at minimal systemic cost when compared with off-optimal control outcome. Therefore, the study not only affirmed the vital concept of optimal control strategy but also, instituted the viability of the model. Thus, this model can be extensively used in Bio-system and applied mathematics.","PeriodicalId":41981,"journal":{"name":"Jordan Journal of Mathematics and Statistics","volume":"3 1","pages":""},"PeriodicalIF":0.3,"publicationDate":"2022-01-01","publicationTypes":"Journal Article","fieldsOfStudy":null,"isOpenAccess":false,"openAccessPdf":"","citationCount":null,"resultStr":null,"platform":"Semanticscholar","paperid":"85879930","PeriodicalName":null,"FirstCategoryId":null,"ListUrlMain":null,"RegionNum":0,"RegionCategory":"","ArticlePicture":[],"TitleCN":null,"AbstractTextCN":null,"PMCID":"","EPubDate":null,"PubModel":null,"JCR":null,"JCRName":null,"Score":null,"Total":0}
Hendrietha Joan Hendricks, J. Ongala, D. Ntirampeba
Corresponding Author: Hendrietha Joan Hendricks Applied Mathematics and Statistics, Namibia University of Science and Technology, Namibia E-mail: theressa.joy.love@gmail.com Abstract: Financial market participants often speculate on how markets would behave in the light of certain information at hand. This speculation contributes to volatility within the financial market and consequently, it makes the market unstable. The Ornstein Uhlenbeck (OU) model has intensively been used in modelling volatility, however, the contribution of speculation on volatility has not been studied in the OU model. Therefore, this study focuses on the modification of the OU model by incorporating a time dependent exponential function that caters for the contribution of speculation on volatility. The statistical properties of the Improved OU model are then studied and the results compared with properties of the OU model. NAD/USD exchange rate data is used to compare and validate the Improved model with the OU model. It was found that both the OU and Improved OU model had a similar expected price, while variance of price for the OU model stabilised upwards up to 16 and variance of price for the Improved OU model stabilised downwards up to 0.01. The variance of the Improved model was found to be much lower than that of the OU model. Additionally, it was found that the distribution of the forecasted price changed with different lead times for the OU model whereas, the distribution of the forecasted price for the Improved OU model did not change with different lead times. Thus, the OU model is a time specific model whereas the Improved OU model is an invariant time model. Consequently, the Improved OU model was found to be more efficient than the OU model.
{"title":"Modification of the Ornstein Uhlenbeck Process to Incorporate the Influence of Speculation on Volatility in Financial Markets","authors":"Hendrietha Joan Hendricks, J. Ongala, D. Ntirampeba","doi":"10.3844/jmssp.2022.1.10","DOIUrl":"https://doi.org/10.3844/jmssp.2022.1.10","url":null,"abstract":"Corresponding Author: Hendrietha Joan Hendricks Applied Mathematics and Statistics, Namibia University of Science and Technology, Namibia E-mail: theressa.joy.love@gmail.com Abstract: Financial market participants often speculate on how markets would behave in the light of certain information at hand. This speculation contributes to volatility within the financial market and consequently, it makes the market unstable. The Ornstein Uhlenbeck (OU) model has intensively been used in modelling volatility, however, the contribution of speculation on volatility has not been studied in the OU model. Therefore, this study focuses on the modification of the OU model by incorporating a time dependent exponential function that caters for the contribution of speculation on volatility. The statistical properties of the Improved OU model are then studied and the results compared with properties of the OU model. NAD/USD exchange rate data is used to compare and validate the Improved model with the OU model. It was found that both the OU and Improved OU model had a similar expected price, while variance of price for the OU model stabilised upwards up to 16 and variance of price for the Improved OU model stabilised downwards up to 0.01. The variance of the Improved model was found to be much lower than that of the OU model. Additionally, it was found that the distribution of the forecasted price changed with different lead times for the OU model whereas, the distribution of the forecasted price for the Improved OU model did not change with different lead times. Thus, the OU model is a time specific model whereas the Improved OU model is an invariant time model. Consequently, the Improved OU model was found to be more efficient than the OU model.","PeriodicalId":41981,"journal":{"name":"Jordan Journal of Mathematics and Statistics","volume":"34 1","pages":""},"PeriodicalIF":0.3,"publicationDate":"2022-01-01","publicationTypes":"Journal Article","fieldsOfStudy":null,"isOpenAccess":false,"openAccessPdf":"","citationCount":null,"resultStr":null,"platform":"Semanticscholar","paperid":"78352492","PeriodicalName":null,"FirstCategoryId":null,"ListUrlMain":null,"RegionNum":0,"RegionCategory":"","ArticlePicture":[],"TitleCN":null,"AbstractTextCN":null,"PMCID":"","EPubDate":null,"PubModel":null,"JCR":null,"JCRName":null,"Score":null,"Total":0}
Pub Date : 2022-01-01DOI: 10.3844/jmssp.2022.16.26
F. Kachapova, Ilias Kachapov
Corresponding Author: Farida Kachapova Department of Mathematical Sciences, Auckland University of Technology, New Zealand E-mail: farida.kachapova@aut.ac.nz Abstract: In this study model of particle motion on a three-dimensional lattice is created using discrete random walk with small steps. A probability space of the particle trajectories is rigorously constructed. Unlike deterministic approach in classical mechanics, here probabilistic properties of particle movement are used to formally derive analogues of Newton’s first and second laws of motion. Similar probabilistic models can potentially be applied to justify laws of thermodynamics in a consistent manner.
{"title":"Elements of Formal Probabilistic Mechanics","authors":"F. Kachapova, Ilias Kachapov","doi":"10.3844/jmssp.2022.16.26","DOIUrl":"https://doi.org/10.3844/jmssp.2022.16.26","url":null,"abstract":"Corresponding Author: Farida Kachapova Department of Mathematical Sciences, Auckland University of Technology, New Zealand E-mail: farida.kachapova@aut.ac.nz Abstract: In this study model of particle motion on a three-dimensional lattice is created using discrete random walk with small steps. A probability space of the particle trajectories is rigorously constructed. Unlike deterministic approach in classical mechanics, here probabilistic properties of particle movement are used to formally derive analogues of Newton’s first and second laws of motion. Similar probabilistic models can potentially be applied to justify laws of thermodynamics in a consistent manner.","PeriodicalId":41981,"journal":{"name":"Jordan Journal of Mathematics and Statistics","volume":"26 1","pages":""},"PeriodicalIF":0.3,"publicationDate":"2022-01-01","publicationTypes":"Journal Article","fieldsOfStudy":null,"isOpenAccess":false,"openAccessPdf":"","citationCount":null,"resultStr":null,"platform":"Semanticscholar","paperid":"73852831","PeriodicalName":null,"FirstCategoryId":null,"ListUrlMain":null,"RegionNum":0,"RegionCategory":"","ArticlePicture":[],"TitleCN":null,"AbstractTextCN":null,"PMCID":"","EPubDate":null,"PubModel":null,"JCR":null,"JCRName":null,"Score":null,"Total":0}
Pub Date : 2022-01-01DOI: 10.3844/jmssp.2022.143.147
M. A. Orukari
: This study considered the Ruin problem with an income process with stationary independent increments. The characterization is obtained which is general for the probability of r ( y ), that the asset of a firm will never be zero whenever the initial asset level of the firm is y . The aim of this study is also to determine r ( y ) = P { T < | Y (0) = y }, If we let T = inf { t ≥ 0; Y ( t ) < 0}, A condition that is necessary and sufficient is studied for a distribution that is one – dimensional of X n which coverages to X * .The result that is obtained concerning the probability, is of ruin before time t . Riemann-Stieltjes integral, two functions f and with symbol as ( ) ( ) b a f x d x was used and is a special case in which () = x , where has a continuous derivative. It is defined such that the Stieltjes integral ( ) ( ) b a f x d x becomes the Riemann integral ( ) ( ) | b a f x x dx .
本研究考虑具有平稳独立增量的收入过程的破产问题。得到了r (y)概率的一般特征，即当企业的初始资产水平为y时，企业的资产永远不会为零。本研究的目的也是确定r (y) = P {T <| y (0) = y}，令T = inf {T≥0;Y (t) < 0}，研究了覆盖到X *的X n的一维分布的一个充要条件，得到了在时间t之前毁灭的概率的结果。使用Riemann-Stieltjes积分，两个函数f和，符号为()()b a f x d x，并且是()= x的特殊情况，其中具有连续导数。它被定义为Stieltjes积分()()b a f x dx变成了Riemann积分()()| b a f x x dx。
{"title":"Mathematical Approach to the Ruin Problem with Compounding Assets","authors":"M. A. Orukari","doi":"10.3844/jmssp.2022.143.147","DOIUrl":"https://doi.org/10.3844/jmssp.2022.143.147","url":null,"abstract":": This study considered the Ruin problem with an income process with stationary independent increments. The characterization is obtained which is general for the probability of r ( y ), that the asset of a firm will never be zero whenever the initial asset level of the firm is y . The aim of this study is also to determine r ( y ) = P { T < | Y (0) = y }, If we let T = inf { t ≥ 0; Y ( t ) < 0}, A condition that is necessary and sufficient is studied for a distribution that is one – dimensional of X n which coverages to X * .The result that is obtained concerning the probability, is of ruin before time t . Riemann-Stieltjes integral, two functions f and with symbol as ( ) ( ) b a f x d x was used and is a special case in which () = x , where has a continuous derivative. It is defined such that the Stieltjes integral ( ) ( ) b a f x d x becomes the Riemann integral ( ) ( ) | b a f x x dx .","PeriodicalId":41981,"journal":{"name":"Jordan Journal of Mathematics and Statistics","volume":"422 1","pages":""},"PeriodicalIF":0.3,"publicationDate":"2022-01-01","publicationTypes":"Journal Article","fieldsOfStudy":null,"isOpenAccess":false,"openAccessPdf":"","citationCount":null,"resultStr":null,"platform":"Semanticscholar","paperid":"77784204","PeriodicalName":null,"FirstCategoryId":null,"ListUrlMain":null,"RegionNum":0,"RegionCategory":"","ArticlePicture":[],"TitleCN":null,"AbstractTextCN":null,"PMCID":"","EPubDate":null,"PubModel":null,"JCR":null,"JCRName":null,"Score":null,"Total":0}
Pub Date : 2022-01-01DOI: 10.3844/jmssp.2022.163.175
Xiao Zhang
: Multivariate probit models have been explored for analyzing longitudinal ordinal data. However, the inherent identification issue in multivariate probit models requires the covariance matrix of the underlying latent multivariate normal variables to be a correlation matrix and thus hinders the development of efficient Bayesian sampling methods. It is known that non-identifiable models may produce Markov Chain Monte Carlo (MCMC) samplers with better convergence and mixing than identifiable models. Therefore, we were motivated to construct a non-identifiable multivariate probit model and to develop efficient MCMC sampling algorithms. In comparison with the MCMC sampling algorithm based on the identifiable multivariate probit model, which requires a Metropolis-Hastings (MH) algorithm for sampling a correlation matrix, our proposed MCMC sampling algorithms based on the non-identifiable model circumvent an MH algorithm by a Gibbs sampler for sampling a covariance matrix and thus accelerate the MCMC convergence. We illustrate our proposed methods using simulation studies and two real data applications. Both the simulation studies and the real data applications show that constructing nonidentifiable models may improve the convergence of the MCMC algorithms compared with the identifiable models. The marginalization of the redundant parameters in the non-identifiable models should be considered in developing efficient MCMC sampling algorithms. This investigation shows that construction of non-identifiable models is valuable in developing MCMC sampling methods and illustrates advantages and disadvantages of construction of non-identifiable models to improve the convergence of the MCMC sampling components.
{"title":"Bayesian Analysis of Longitudinal Ordinal Data Using Non-Identifiable Multivariate Probit Models","authors":"Xiao Zhang","doi":"10.3844/jmssp.2022.163.175","DOIUrl":"https://doi.org/10.3844/jmssp.2022.163.175","url":null,"abstract":": Multivariate probit models have been explored for analyzing longitudinal ordinal data. However, the inherent identification issue in multivariate probit models requires the covariance matrix of the underlying latent multivariate normal variables to be a correlation matrix and thus hinders the development of efficient Bayesian sampling methods. It is known that non-identifiable models may produce Markov Chain Monte Carlo (MCMC) samplers with better convergence and mixing than identifiable models. Therefore, we were motivated to construct a non-identifiable multivariate probit model and to develop efficient MCMC sampling algorithms. In comparison with the MCMC sampling algorithm based on the identifiable multivariate probit model, which requires a Metropolis-Hastings (MH) algorithm for sampling a correlation matrix, our proposed MCMC sampling algorithms based on the non-identifiable model circumvent an MH algorithm by a Gibbs sampler for sampling a covariance matrix and thus accelerate the MCMC convergence. We illustrate our proposed methods using simulation studies and two real data applications. Both the simulation studies and the real data applications show that constructing nonidentifiable models may improve the convergence of the MCMC algorithms compared with the identifiable models. The marginalization of the redundant parameters in the non-identifiable models should be considered in developing efficient MCMC sampling algorithms. This investigation shows that construction of non-identifiable models is valuable in developing MCMC sampling methods and illustrates advantages and disadvantages of construction of non-identifiable models to improve the convergence of the MCMC sampling components.","PeriodicalId":41981,"journal":{"name":"Jordan Journal of Mathematics and Statistics","volume":"57 1","pages":""},"PeriodicalIF":0.3,"publicationDate":"2022-01-01","publicationTypes":"Journal Article","fieldsOfStudy":null,"isOpenAccess":false,"openAccessPdf":"","citationCount":null,"resultStr":null,"platform":"Semanticscholar","paperid":"76152171","PeriodicalName":null,"FirstCategoryId":null,"ListUrlMain":null,"RegionNum":0,"RegionCategory":"","ArticlePicture":[],"TitleCN":null,"AbstractTextCN":null,"PMCID":"","EPubDate":null,"PubModel":null,"JCR":null,"JCRName":null,"Score":null,"Total":0}
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