Pub Date : 2024-03-22DOI: 10.9734/jamcs/2024/v39i41879
S. Guritman, Jaharuddin, Teduh Wulandari, Siswandi
In this article, the inverse including the determinant, and the eigenvalues of circulant matrices with entry Lucas numbers are formulated explicitly in a simple way so that their computations can be constructed efficiently. The formulation method of the determinant and inverse is simply applying the theory of elementary row or column operations and can be unified in one theorem. Meanwhile, for the eigenvalues formulation, the recently known formulation in the case of general circulant matrices is simplified by observing the specialty of the Lucas sequence and applying cyclic group properties of unit circles in the complex plane. Then, an algorithm of those formulations is constructed efficiently. From some implementation facts also showed that the algorithms performed very fast and was able to calculate large size of circulant matrices.
{"title":"An Efficient Method for Computing the Inverse and Eigenvalues of Circulant Matrices with Lucas Numbers","authors":"S. Guritman, Jaharuddin, Teduh Wulandari, Siswandi","doi":"10.9734/jamcs/2024/v39i41879","DOIUrl":"https://doi.org/10.9734/jamcs/2024/v39i41879","url":null,"abstract":"In this article, the inverse including the determinant, and the eigenvalues of circulant matrices with entry Lucas numbers are formulated explicitly in a simple way so that their computations can be constructed efficiently. The formulation method of the determinant and inverse is simply applying the theory of elementary row or column operations and can be unified in one theorem. Meanwhile, for the eigenvalues formulation, the recently known formulation in the case of general circulant matrices is simplified by observing the specialty of the Lucas sequence and applying cyclic group properties of unit circles in the complex plane. Then, an algorithm of those formulations is constructed efficiently. From some implementation facts also showed that the algorithms performed very fast and was able to calculate large size of circulant matrices.","PeriodicalId":503149,"journal":{"name":"Journal of Advances in Mathematics and Computer Science","volume":" 3","pages":""},"PeriodicalIF":0.0,"publicationDate":"2024-03-22","publicationTypes":"Journal Article","fieldsOfStudy":null,"isOpenAccess":false,"openAccessPdf":"","citationCount":null,"resultStr":null,"platform":"Semanticscholar","paperid":"140212189","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 : 2024-03-11DOI: 10.9734/jamcs/2024/v39i31877
Sergio Falcon
In this paper, we study the iterated convolution of the k-Lucas sequences in a form similar to the iterated convolution of the k-Fibonacci sequences [1]. A particular case is for the self-convolution of these sequences. Moreover, the generating functions of all these convolved sequences, we find the recurrence relation between the terms of the resulting sequences.
{"title":"On the Convolution of the k-Lucas Sequences","authors":"Sergio Falcon","doi":"10.9734/jamcs/2024/v39i31877","DOIUrl":"https://doi.org/10.9734/jamcs/2024/v39i31877","url":null,"abstract":"In this paper, we study the iterated convolution of the k-Lucas sequences in a form similar to the iterated convolution of the k-Fibonacci sequences [1]. \u0000A particular case is for the self-convolution of these sequences. Moreover, the generating functions of all these convolved sequences, we find the recurrence relation between the terms of the resulting sequences.","PeriodicalId":503149,"journal":{"name":"Journal of Advances in Mathematics and Computer Science","volume":"11 9","pages":""},"PeriodicalIF":0.0,"publicationDate":"2024-03-11","publicationTypes":"Journal Article","fieldsOfStudy":null,"isOpenAccess":false,"openAccessPdf":"","citationCount":null,"resultStr":null,"platform":"Semanticscholar","paperid":"140252495","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 : 2024-03-11DOI: 10.9734/jamcs/2024/v39i41878
Calvince Fwaga, Wilys O. Mukuna, Levi Otanga Olwamba
Over the years studies have been done on option pricing valuation. The world market economies have experienced tremendous asset price uctuations since 1980s. For this reason, efforts have been directed towards developing reliable and more accurate option pricing models. Black-Scholes-Merton model has so far been proved to be the most powerful and significant tool for the valuation of an option. However, its assumption of zero transaction cost on asset pricing yields inaccurate option values. The study investigates the effects of transaction cost on call and put option of an asset price using a two-dimensional Black-Scholes-Merton partial differential equation. The Dufort-Frankel Finite Difference Method is used to approximate the solution to the BSM model equation describing the value of an option with boundary conditions. The simulation is done with the aid of MATLAB software program. The effects of incorporating transaction cost on the two assets prices on the value of an option using BSMPDE are determined. From the study, it is established that as transaction cost increases, the call and put option values decrease. The effects of incorporating transaction cost on the values of call and put option are shown in tabular form and graphically. These results are useful to the investors in computing possible returns on investment based on more accurate asset pricing and to the government on policy formulation in controlling prices in stock exchange market.
{"title":"Mathematical Investigation of Option Pricing using Black- Scholes-Merton Partial Differential Equation with Transaction Cost","authors":"Calvince Fwaga, Wilys O. Mukuna, Levi Otanga Olwamba","doi":"10.9734/jamcs/2024/v39i41878","DOIUrl":"https://doi.org/10.9734/jamcs/2024/v39i41878","url":null,"abstract":"Over the years studies have been done on option pricing valuation. The world market economies have experienced tremendous asset price uctuations since 1980s. For this reason, efforts have been directed towards developing reliable and more accurate option pricing models. Black-Scholes-Merton model has so far been proved to be the most powerful and significant tool for the valuation of an option. However, its assumption of zero transaction cost on asset pricing yields inaccurate option values. The study investigates the effects of transaction cost on call and put option of an asset price using a two-dimensional Black-Scholes-Merton partial differential equation. The Dufort-Frankel Finite Difference Method is used to approximate the solution to the BSM model equation describing the value of an option with boundary conditions. The simulation is done with the aid of MATLAB software program. The effects of incorporating transaction cost on the two assets prices on the value of an option using BSMPDE are determined. From the study, it is established that as transaction cost increases, the call and put option values decrease. The effects of incorporating transaction cost on the values of call and put option are shown in tabular form and graphically. These results are useful to the investors in computing possible returns on investment based on more accurate asset pricing and to the government on policy formulation in controlling prices in stock exchange market.\u0000 ","PeriodicalId":503149,"journal":{"name":"Journal of Advances in Mathematics and Computer Science","volume":"122 4","pages":""},"PeriodicalIF":0.0,"publicationDate":"2024-03-11","publicationTypes":"Journal Article","fieldsOfStudy":null,"isOpenAccess":false,"openAccessPdf":"","citationCount":null,"resultStr":null,"platform":"Semanticscholar","paperid":"140251546","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 : 2024-03-09DOI: 10.9734/jamcs/2024/v39i31876
Sergio Falcon
This paper studies an extension of the classical Padovan sequence and that contains this as a particular case. Some very interesting formulas are found for the sum of these new sequences, for the sum of their squares as well as their self-convolution.
{"title":"On a Generalization of the Padovan Numbers","authors":"Sergio Falcon","doi":"10.9734/jamcs/2024/v39i31876","DOIUrl":"https://doi.org/10.9734/jamcs/2024/v39i31876","url":null,"abstract":"This paper studies an extension of the classical Padovan sequence and that contains this as a particular case. Some very interesting formulas are found for the sum of these new sequences, for the sum of their squares as well as their self-convolution.","PeriodicalId":503149,"journal":{"name":"Journal of Advances in Mathematics and Computer Science","volume":"49 12","pages":""},"PeriodicalIF":0.0,"publicationDate":"2024-03-09","publicationTypes":"Journal Article","fieldsOfStudy":null,"isOpenAccess":false,"openAccessPdf":"","citationCount":null,"resultStr":null,"platform":"Semanticscholar","paperid":"140255517","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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