Pub Date : 2021-04-29DOI: 10.37394/23206.2021.20.21
D. K. Nagar, E. Zarrazola, A. Roldán-Correa
The Kummer-gamma distribution is an extension of gamma distribution and for certain values of parameters slides to a bimodal distribution. In this article, we introduce a bivariate distribution with Kummer-gamma conditionals and call it the conditionally specified bivariate Kummer-gamma distribution/bivariate Kummer-gamma conditionals distribution. Various representations are derived for its product moments, marginal densities, marginal moments, conditional densities, and conditional moments. We also discuss several important properties including, entropies, distributions of sum, and quotient. Most of these representations involve special functions such as the Gauss and the confluent hypergeometric functions. The bivariate Kummer-gamma conditionals distribution studied in this article may serve as an alternative to many existing bivariate models with support on (0,∞)× (0,∞). Key-Words: Bivariate distribution; confluent hypergeometric function; gamma distribution; gamma function; Gauss hypergeometric function; Kummer-gamma distribution. Received: March 20, 2021. Revised: April 20, 2021. Accepted: April 22, 2021. Published: April 29, 2021.
{"title":"Conditionally Specified Bivariate Kummer-Gamma Distribution","authors":"D. K. Nagar, E. Zarrazola, A. Roldán-Correa","doi":"10.37394/23206.2021.20.21","DOIUrl":"https://doi.org/10.37394/23206.2021.20.21","url":null,"abstract":"The Kummer-gamma distribution is an extension of gamma distribution and for certain values of parameters slides to a bimodal distribution. In this article, we introduce a bivariate distribution with Kummer-gamma conditionals and call it the conditionally specified bivariate Kummer-gamma distribution/bivariate Kummer-gamma conditionals distribution. Various representations are derived for its product moments, marginal densities, marginal moments, conditional densities, and conditional moments. We also discuss several important properties including, entropies, distributions of sum, and quotient. Most of these representations involve special functions such as the Gauss and the confluent hypergeometric functions. The bivariate Kummer-gamma conditionals distribution studied in this article may serve as an alternative to many existing bivariate models with support on (0,∞)× (0,∞). Key-Words: Bivariate distribution; confluent hypergeometric function; gamma distribution; gamma function; Gauss hypergeometric function; Kummer-gamma distribution. Received: March 20, 2021. Revised: April 20, 2021. Accepted: April 22, 2021. Published: April 29, 2021.","PeriodicalId":112268,"journal":{"name":"WSEAS Transactions on Mathematics archive","volume":"13 1","pages":"0"},"PeriodicalIF":0.0,"publicationDate":"2021-04-29","publicationTypes":"Journal Article","fieldsOfStudy":null,"isOpenAccess":false,"openAccessPdf":"","citationCount":null,"resultStr":null,"platform":"Semanticscholar","paperid":"127943463","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 : 2021-04-21DOI: 10.37394/23206.2021.20.19
Radwan Abu Gdairi, I. Noaman
Fuzzy set theory and fuzzy relation are important techniques in knowledge discovery in databases. In this work, we presented fuzzy sets and fuzzy relations according to some giving Information by using rough membership function as a new way to get fuzzy set and fuzzy relation to help the decision in any topic . Some properties have been studied. And application of my life on the fuzzy set was introduced.
{"title":"Generating Fuzzy Sets and Fuzzy Relations Based on Information","authors":"Radwan Abu Gdairi, I. Noaman","doi":"10.37394/23206.2021.20.19","DOIUrl":"https://doi.org/10.37394/23206.2021.20.19","url":null,"abstract":"Fuzzy set theory and fuzzy relation are important techniques in knowledge discovery in databases. In this work, we presented fuzzy sets and fuzzy relations according to some giving Information by using rough membership function as a new way to get fuzzy set and fuzzy relation to help the decision in any topic . Some properties have been studied. And application of my life on the fuzzy set was introduced.","PeriodicalId":112268,"journal":{"name":"WSEAS Transactions on Mathematics archive","volume":"1 1","pages":"0"},"PeriodicalIF":0.0,"publicationDate":"2021-04-21","publicationTypes":"Journal Article","fieldsOfStudy":null,"isOpenAccess":false,"openAccessPdf":"","citationCount":null,"resultStr":null,"platform":"Semanticscholar","paperid":"131271118","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 : 2021-04-09DOI: 10.37394/23206.2021.20.18
O. Karelin, A. Tarasenko
Problems of factorization of matrix functions are closely connected with the solution of matrix Riemann boundary value problems and with the solution of vector singular integral equations. In this article, we study functional operators with orientation-reversing shift reflection on the real axes. We introduce the concept of multiplicative representation of functional operators with shift and its partial indices. Based on the classical notion of matrix factorization, the correctness of the definitions is shown. A theorem on the relationship between factorization of functional operators with reflection and factorization of the corresponding matrix functions is proven. Key-Words: Factorization, Functional operators, Carleman shift, Reflection, Matrix Riemann boundary value Problem, Partial indices, Operator identities Received: January 24, 2021. Revised: April 2, 2021. Accepted: April 6, 2021. Published: April 9, 2021.
{"title":"On Factorization of Functional Operators with Reflection on the Real Axis","authors":"O. Karelin, A. Tarasenko","doi":"10.37394/23206.2021.20.18","DOIUrl":"https://doi.org/10.37394/23206.2021.20.18","url":null,"abstract":"Problems of factorization of matrix functions are closely connected with the solution of matrix Riemann boundary value problems and with the solution of vector singular integral equations. In this article, we study functional operators with orientation-reversing shift reflection on the real axes. We introduce the concept of multiplicative representation of functional operators with shift and its partial indices. Based on the classical notion of matrix factorization, the correctness of the definitions is shown. A theorem on the relationship between factorization of functional operators with reflection and factorization of the corresponding matrix functions is proven. Key-Words: Factorization, Functional operators, Carleman shift, Reflection, Matrix Riemann boundary value Problem, Partial indices, Operator identities Received: January 24, 2021. Revised: April 2, 2021. Accepted: April 6, 2021. Published: April 9, 2021.","PeriodicalId":112268,"journal":{"name":"WSEAS Transactions on Mathematics archive","volume":"BC-29 1","pages":"0"},"PeriodicalIF":0.0,"publicationDate":"2021-04-09","publicationTypes":"Journal Article","fieldsOfStudy":null,"isOpenAccess":false,"openAccessPdf":"","citationCount":null,"resultStr":null,"platform":"Semanticscholar","paperid":"126717866","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 : 2021-04-09DOI: 10.37394/23206.2021.20.17
K. Chanthawara, S. Kaennakham
The so-called Dual Reciprocity Boundary Element Method (DRBEM) has been a popular alternative scheme designed to alleviate problems encountered when using the traditional BEM for numerically solving engineering problems that are described by PDEs. The method starts with writing the right-hand-side of Poisson equation as a summation of a pre-chosen multivariate function known as ‘Radial Basis Function (RBF)’. Nevertheless, a common undesirable feature of using RBFs is the appearance of the so-called ‘shape parameter’ whose value greatly affects the solution accuracy. In this work, a new form of RBF containing no shape (so that it can be called ‘shapefree/shapeless’) is invented, proposed and applied in conjunction with DRBEM is validated numerically. The solutions obtained are compared against both exact ones and those presented in literature where appropriate, for validation. It is found that reasonably and comparatively good approximated solutions of PDEs can still be obtained without the difficulty of choosing a good shape for RBF used. Key-Words: Dual reciprocity, Boundary element method, Shapeless parameter, Radial basis function, Partial differential equation, Numerical solution Received: January 21, 2021. Revised: April 1, 2021. Accepted: April 5, 2021. Published: April 9, 2021.
所谓的双互易边界元法(Dual Reciprocity Boundary Element Method, DRBEM)是一种流行的替代方案，旨在缓解使用传统边界元法数值求解由偏微分方程描述的工程问题时遇到的问题。该方法首先将泊松方程的右侧写成预先选择的多元函数的求和，称为“径向基函数(RBF)”。然而，使用rbf的一个常见的不受欢迎的特征是所谓的“形状参数”的出现，其值极大地影响了解的精度。在这项工作中，发明了一种新的不含形状的RBF(因此它可以被称为“无形状/无形状”)，提出并与DRBEM结合应用，并进行了数值验证。在适当的情况下，将得到的解与精确解和文献中提出的解进行比较，以进行验证。结果表明，在不存在选择合适径向基形状的困难的情况下，仍然可以得到较为合理和较好的偏微分方程近似解。关键词:对偶互易，边界元法，无形参数，径向基函数，偏微分方程，数值解修订日期:2021年4月1日。录用日期:2021年4月5日。发布日期:2021年4月9日。
{"title":"A Hybrid Shapeless Radial Basis Function Applied With the Dual Reciprocity Boundary Element Method","authors":"K. Chanthawara, S. Kaennakham","doi":"10.37394/23206.2021.20.17","DOIUrl":"https://doi.org/10.37394/23206.2021.20.17","url":null,"abstract":"The so-called Dual Reciprocity Boundary Element Method (DRBEM) has been a popular alternative scheme designed to alleviate problems encountered when using the traditional BEM for numerically solving engineering problems that are described by PDEs. The method starts with writing the right-hand-side of Poisson equation as a summation of a pre-chosen multivariate function known as ‘Radial Basis Function (RBF)’. Nevertheless, a common undesirable feature of using RBFs is the appearance of the so-called ‘shape parameter’ whose value greatly affects the solution accuracy. In this work, a new form of RBF containing no shape (so that it can be called ‘shapefree/shapeless’) is invented, proposed and applied in conjunction with DRBEM is validated numerically. The solutions obtained are compared against both exact ones and those presented in literature where appropriate, for validation. It is found that reasonably and comparatively good approximated solutions of PDEs can still be obtained without the difficulty of choosing a good shape for RBF used. Key-Words: Dual reciprocity, Boundary element method, Shapeless parameter, Radial basis function, Partial differential equation, Numerical solution Received: January 21, 2021. Revised: April 1, 2021. Accepted: April 5, 2021. Published: April 9, 2021.","PeriodicalId":112268,"journal":{"name":"WSEAS Transactions on Mathematics archive","volume":"52 1","pages":"0"},"PeriodicalIF":0.0,"publicationDate":"2021-04-09","publicationTypes":"Journal Article","fieldsOfStudy":null,"isOpenAccess":false,"openAccessPdf":"","citationCount":null,"resultStr":null,"platform":"Semanticscholar","paperid":"117106614","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 : 2021-04-09DOI: 10.37394/23206.2021.20.16
E. Almuhur, M. Al-Labadi
The main purposes of this article is to introduce new generalizations of the notion of pairwise Lindelöf spaces in bitopological spaces where new notions: pairwise strongly Lindelöf, pairwise nearly, pairwise almost and pairwise weakly strongly Lindelöf bitopological spaces depend on the new notion pairwise preopen countable covers. These covers where we focused on their importance in topology consist of countable subfamilies whose closures cover the bitopological spaces and we clarified how pairwise preopen countable covers effect on pairwise strongly Lindelöf spaces. The new concepts of pairwise strongly Lindelöf, pairwise nearly, pairwise almost and pairwise weakly strongly Lindelöf bitopological spaces are introduced and many definitions, propositions, characterizations and remarks concerning those notions are initiated, discussed and explored. Furthermore, the relationships between those bitopological spaces are examined and investigated. We illustrated the implications hold by these new bitopological spaces. We put some queries and claims, then we struggle to provide their proofs. Key-Words: Pairwise Strongly Lindelöf, Pairwise Almost Strongly Lindelöf. Received: January 16, 2021. Revised: April 1, 2021. Accepted: April 5, 2021. Published: April 9, 2021.
{"title":"Pairwise Strongly Lindelöf, Pairwise Nearly, Almost and Weakly Lindelöf Bitopological Spaces","authors":"E. Almuhur, M. Al-Labadi","doi":"10.37394/23206.2021.20.16","DOIUrl":"https://doi.org/10.37394/23206.2021.20.16","url":null,"abstract":"The main purposes of this article is to introduce new generalizations of the notion of pairwise Lindelöf spaces in bitopological spaces where new notions: pairwise strongly Lindelöf, pairwise nearly, pairwise almost and pairwise weakly strongly Lindelöf bitopological spaces depend on the new notion pairwise preopen countable covers. These covers where we focused on their importance in topology consist of countable subfamilies whose closures cover the bitopological spaces and we clarified how pairwise preopen countable covers effect on pairwise strongly Lindelöf spaces. The new concepts of pairwise strongly Lindelöf, pairwise nearly, pairwise almost and pairwise weakly strongly Lindelöf bitopological spaces are introduced and many definitions, propositions, characterizations and remarks concerning those notions are initiated, discussed and explored. Furthermore, the relationships between those bitopological spaces are examined and investigated. We illustrated the implications hold by these new bitopological spaces. We put some queries and claims, then we struggle to provide their proofs. Key-Words: Pairwise Strongly Lindelöf, Pairwise Almost Strongly Lindelöf. Received: January 16, 2021. Revised: April 1, 2021. Accepted: April 5, 2021. Published: April 9, 2021.","PeriodicalId":112268,"journal":{"name":"WSEAS Transactions on Mathematics archive","volume":"101 1","pages":"0"},"PeriodicalIF":0.0,"publicationDate":"2021-04-09","publicationTypes":"Journal Article","fieldsOfStudy":null,"isOpenAccess":false,"openAccessPdf":"","citationCount":null,"resultStr":null,"platform":"Semanticscholar","paperid":"115667620","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 : 2021-04-06DOI: 10.37394/23206.2021.20.14
A. S. Al-Moisheer, A. Daghestani, K. S. Sultan
In this paper, we talk about a mixture of one-parameter Lindley and inverse Weibull distributions (MLIWD). First, We introduce and discuss the MLIWD. Then, we study the main statistical properties of the proposed mixture and provide some graphs of both the density and the associated hazard rate functions. After that, we estimate the unknown parameters of the proposed mixture via two estimation methods, namely, the generalized method of moments and maximum likelihood. In addition, we compare the estimation methods via some simulation studies to determine the efficacy of the two estimation methods. Finally, we evaluate the performance and behavior of the proposed mixture with different numerical examples and real data application in survival analysis.
{"title":"Mixture of Lindley and Inverse Weibull Distributions: Properties and Estimation","authors":"A. S. Al-Moisheer, A. Daghestani, K. S. Sultan","doi":"10.37394/23206.2021.20.14","DOIUrl":"https://doi.org/10.37394/23206.2021.20.14","url":null,"abstract":"In this paper, we talk about a mixture of one-parameter Lindley and inverse Weibull distributions (MLIWD). First, We introduce and discuss the MLIWD. Then, we study the main statistical properties of the proposed mixture and provide some graphs of both the density and the associated hazard rate functions. After that, we estimate the unknown parameters of the proposed mixture via two estimation methods, namely, the generalized method of moments and maximum likelihood. In addition, we compare the estimation methods via some simulation studies to determine the efficacy of the two estimation methods. Finally, we evaluate the performance and behavior of the proposed mixture with different numerical examples and real data application in survival analysis.","PeriodicalId":112268,"journal":{"name":"WSEAS Transactions on Mathematics archive","volume":"51 1","pages":"0"},"PeriodicalIF":0.0,"publicationDate":"2021-04-06","publicationTypes":"Journal Article","fieldsOfStudy":null,"isOpenAccess":false,"openAccessPdf":"","citationCount":null,"resultStr":null,"platform":"Semanticscholar","paperid":"129721278","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 : 2021-04-06DOI: 10.37394/23206.2021.20.15
O. Ferrer, Luis Lazaro, J. Rodríguez
A definition of Bessel’s sequences in spaces with an indefinite metric is introduced as a generalization of Bessel’s sequences in Hilbert spaces. Moreover, a complete characterization of Bessel’s sequences in the Hilbert space associated to a space with an indefinite metric is given. The fundamental tools of Bessel’s sequences theory are described in the formalism of spaces with an indefinite metric. It is shown how to construct a Bessel’s sequences in spaces with an indefinite metric starting from a pair of Hilbert spaces, a condition is given to decompose a Bessel’s sequences into in spaces with an indefinite metric so that this decomposition generates a pair of Bessel’s sequences for the Hilbert spaces corresponding to the fundamental decomposition. In spaces where there was no norm, it seemed impossible to construct Bessel’s sequences. The fact that in [1] frame were constructed for Krein spaces motivated us to construct Bessel’s sequences for spaces of indefinite metric. Key-Words: Krein spaces, indefinite metric, J −norm, successions de J −Bessel, base J −orthonormal. Received: January 20, 2021. Revised: March 29, 2021. Accepted: April 2, 2021. Published: April 6, 2021.
{"title":"Successions of J-bessel in Spaces with Indefinite Metric","authors":"O. Ferrer, Luis Lazaro, J. Rodríguez","doi":"10.37394/23206.2021.20.15","DOIUrl":"https://doi.org/10.37394/23206.2021.20.15","url":null,"abstract":"A definition of Bessel’s sequences in spaces with an indefinite metric is introduced as a generalization of Bessel’s sequences in Hilbert spaces. Moreover, a complete characterization of Bessel’s sequences in the Hilbert space associated to a space with an indefinite metric is given. The fundamental tools of Bessel’s sequences theory are described in the formalism of spaces with an indefinite metric. It is shown how to construct a Bessel’s sequences in spaces with an indefinite metric starting from a pair of Hilbert spaces, a condition is given to decompose a Bessel’s sequences into in spaces with an indefinite metric so that this decomposition generates a pair of Bessel’s sequences for the Hilbert spaces corresponding to the fundamental decomposition. In spaces where there was no norm, it seemed impossible to construct Bessel’s sequences. The fact that in [1] frame were constructed for Krein spaces motivated us to construct Bessel’s sequences for spaces of indefinite metric. Key-Words: Krein spaces, indefinite metric, J −norm, successions de J −Bessel, base J −orthonormal. Received: January 20, 2021. Revised: March 29, 2021. Accepted: April 2, 2021. Published: April 6, 2021.","PeriodicalId":112268,"journal":{"name":"WSEAS Transactions on Mathematics archive","volume":"1 1","pages":"0"},"PeriodicalIF":0.0,"publicationDate":"2021-04-06","publicationTypes":"Journal Article","fieldsOfStudy":null,"isOpenAccess":false,"openAccessPdf":"","citationCount":null,"resultStr":null,"platform":"Semanticscholar","paperid":"130006732","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 : 2021-04-02DOI: 10.37394/23206.2021.20.11
Supitcha Mamuangbon, K. Budsaba, Andrei Volodin
In this research, we propose a new four parameter family of distributions called Generalized Crack distribution. We generalizes the family three parameter Crack distribution. The Generalized Crack distribution is a mixture of two parameter Inverse Gaussian distribution, Length-Biased Inverse Gaussian distribution, Twice Length-Biased Inverse Gaussian distribution, and adding one more weight parameter . It is a special case for , where and is the weighted parameter. We investigate the properties of Generalized Crack distribution including first four moments, parameters estimation by using the maximum likelihood estimators and method of moment estimation. Evaluate the performance of the estimators by using bias. The results of simulation are presented in numerically and graphically.
{"title":"The Performance of Estimators for Generalization of Crack Distribution","authors":"Supitcha Mamuangbon, K. Budsaba, Andrei Volodin","doi":"10.37394/23206.2021.20.11","DOIUrl":"https://doi.org/10.37394/23206.2021.20.11","url":null,"abstract":"In this research, we propose a new four parameter family of distributions called Generalized Crack distribution. We generalizes the family three parameter Crack distribution. The Generalized Crack distribution is a mixture of two parameter Inverse Gaussian distribution, Length-Biased Inverse Gaussian distribution, Twice Length-Biased Inverse Gaussian distribution, and adding one more weight parameter . It is a special case for , where and is the weighted parameter. We investigate the properties of Generalized Crack distribution including first four moments, parameters estimation by using the maximum likelihood estimators and method of moment estimation. Evaluate the performance of the estimators by using bias. The results of simulation are presented in numerically and graphically.","PeriodicalId":112268,"journal":{"name":"WSEAS Transactions on Mathematics archive","volume":"17 1","pages":"0"},"PeriodicalIF":0.0,"publicationDate":"2021-04-02","publicationTypes":"Journal Article","fieldsOfStudy":null,"isOpenAccess":false,"openAccessPdf":"","citationCount":null,"resultStr":null,"platform":"Semanticscholar","paperid":"115829000","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 : 2021-04-02DOI: 10.37394/23206.2021.20.13
Sorrawee Roenganan, Masnita Misran, N. Phewchean
Life insurance, not included as a part of the legal obligation in some countries, is one of the investment approaches that might not stand high in the public favor for some people since this is a type of investments that the investor cannot know beforehand the exact return, and the returns completely depend on uncertainty of the policy specification in some circumstances. Similar to the other kinds of investment, investors in life insurance products have been seeking a tool for investment evaluation. However, currently there are no accurate tools that can provide the value of the investment in a life insurance product sensitive to the uncertainty. Internal rate of return is the basic tool that buyers or bankers may apply in order to find the rate of return of this type of investment. The investment decision tool is one of the most important keys that investors have utilized upon making their decisions on investments. Therefore, in this research, we propose a new mathematical model with applications for investment decision, being an extension of the internal rate of return by taking into account the life probability, considering different types of life insurance policies, and other factors specified on life insurance investments such as the premium, the death benefit, the maturity value, the sum insured, the lapse rate, the surrender value, the annuity certain, and the lapse rate with different genders and ages. This newly proposed model is named as the "Life Internal Rate of Return" or Life-IRR model. By using the sample data for both males and females aged 30 years old with expected benefit of 100,000 baht for different types of life insurance policies which are endowment plan, whole life plan and retirement plan, the results show that, for males, the highest life rate of returns is that obtained from the retirement plan (3.633692%), and the lowest life internal rates of returns is that obtained from the endowment plan (2.384443%), while the whole life plan offers moderate life rate of returns of 2.427941%. For females, the highest life rate of returns is that obtained from the retirement plan (3.335189%), and the lowest life internal rates of returns is that obtained from the whole life plan (2.104658%), while the endowment plan offers moderate life rate of returns of 2.308062%. The sensitivity analyses of the life internal rates of return perform the natural characteristics of life insurance. Key-Words: Life internal rate of return, Internal rate of return, Net present value, Life insurance. Received: February 28, 2021. Revised: March 26, 2021. Accepted: March 30, 2021. Published: April 2, 2021.
{"title":"A Study of Life Internal Rate of Return","authors":"Sorrawee Roenganan, Masnita Misran, N. Phewchean","doi":"10.37394/23206.2021.20.13","DOIUrl":"https://doi.org/10.37394/23206.2021.20.13","url":null,"abstract":"Life insurance, not included as a part of the legal obligation in some countries, is one of the investment approaches that might not stand high in the public favor for some people since this is a type of investments that the investor cannot know beforehand the exact return, and the returns completely depend on uncertainty of the policy specification in some circumstances. Similar to the other kinds of investment, investors in life insurance products have been seeking a tool for investment evaluation. However, currently there are no accurate tools that can provide the value of the investment in a life insurance product sensitive to the uncertainty. Internal rate of return is the basic tool that buyers or bankers may apply in order to find the rate of return of this type of investment. The investment decision tool is one of the most important keys that investors have utilized upon making their decisions on investments. Therefore, in this research, we propose a new mathematical model with applications for investment decision, being an extension of the internal rate of return by taking into account the life probability, considering different types of life insurance policies, and other factors specified on life insurance investments such as the premium, the death benefit, the maturity value, the sum insured, the lapse rate, the surrender value, the annuity certain, and the lapse rate with different genders and ages. This newly proposed model is named as the \"Life Internal Rate of Return\" or Life-IRR model. By using the sample data for both males and females aged 30 years old with expected benefit of 100,000 baht for different types of life insurance policies which are endowment plan, whole life plan and retirement plan, the results show that, for males, the highest life rate of returns is that obtained from the retirement plan (3.633692%), and the lowest life internal rates of returns is that obtained from the endowment plan (2.384443%), while the whole life plan offers moderate life rate of returns of 2.427941%. For females, the highest life rate of returns is that obtained from the retirement plan (3.335189%), and the lowest life internal rates of returns is that obtained from the whole life plan (2.104658%), while the endowment plan offers moderate life rate of returns of 2.308062%. The sensitivity analyses of the life internal rates of return perform the natural characteristics of life insurance. Key-Words: Life internal rate of return, Internal rate of return, Net present value, Life insurance. Received: February 28, 2021. Revised: March 26, 2021. Accepted: March 30, 2021. Published: April 2, 2021.","PeriodicalId":112268,"journal":{"name":"WSEAS Transactions on Mathematics archive","volume":"45 1","pages":"0"},"PeriodicalIF":0.0,"publicationDate":"2021-04-02","publicationTypes":"Journal Article","fieldsOfStudy":null,"isOpenAccess":false,"openAccessPdf":"","citationCount":null,"resultStr":null,"platform":"Semanticscholar","paperid":"122109103","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 : 2021-04-02DOI: 10.37394/23206.2021.20.12
Somphorn Arunsingkarat, R. Costa, Masnita Misran, N. Phewchean
Variance changes over time and depends on historical data and previous variances; as a result, it is useful to use a GARCH process to model it. In this paper, we use the notion of Conditional Esscher transform to GARCH models to find the GARCH, EGARCH and GJR risk-neutral models. Subsequently, we apply these three models to obtain option prices for the Stock Exchange of Thailand and compare to the well-known Black-Scholes model. Findings suggest that most of the pricing options under GARCH model are the nearest to the actual prices for SET50 option contracts with both times to maturity of 30 days and 60 days. Key-Words: Option pricing, GARCH model, Stochastic assets. Received: March 1, 2021. Revised: March 24, 2021. Accepted: March 28, 2021. Published: April 2, 2021.
{"title":"Option Pricing Under GARCH Models Applied to the SET50 Index of Thailand","authors":"Somphorn Arunsingkarat, R. Costa, Masnita Misran, N. Phewchean","doi":"10.37394/23206.2021.20.12","DOIUrl":"https://doi.org/10.37394/23206.2021.20.12","url":null,"abstract":"Variance changes over time and depends on historical data and previous variances; as a result, it is useful to use a GARCH process to model it. In this paper, we use the notion of Conditional Esscher transform to GARCH models to find the GARCH, EGARCH and GJR risk-neutral models. Subsequently, we apply these three models to obtain option prices for the Stock Exchange of Thailand and compare to the well-known Black-Scholes model. Findings suggest that most of the pricing options under GARCH model are the nearest to the actual prices for SET50 option contracts with both times to maturity of 30 days and 60 days. Key-Words: Option pricing, GARCH model, Stochastic assets. Received: March 1, 2021. Revised: March 24, 2021. Accepted: March 28, 2021. Published: April 2, 2021.","PeriodicalId":112268,"journal":{"name":"WSEAS Transactions on Mathematics archive","volume":"66 1","pages":"0"},"PeriodicalIF":0.0,"publicationDate":"2021-04-02","publicationTypes":"Journal Article","fieldsOfStudy":null,"isOpenAccess":false,"openAccessPdf":"","citationCount":null,"resultStr":null,"platform":"Semanticscholar","paperid":"132625658","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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