When the insurance benefit of a last-survivor insurance product is payable at the moment of the last insured death, exploring continuous mortality models is essential to obtain the most appropriate premium and benefit reserve. In this study, Gamma-Gompertz mortality law was applied to Indonesian population mortality data at adulthood and old age stages to calculate the annual gross premium and gross benefit reserve of a whole life last survivor insurance product. The annual gross premium was computed using the actuarial equivalence principle. Results show that the older the policyholders purchase the product, the higher the annual gross premium they must pay. The gross benefit reserve needed to be set by the insurance company for the whole life last survivor insurance product was calculated using the prospective method. Its value grows for each valuation year until it approaches the insurance benefit amount.
{"title":"Last-Survivor Insurance Premium and Benefit Reserve Calculation using Gamma-Gompertz Mortality Law","authors":"Ruhiyat Ruhiyat, Windiani Erliana, Kenzi Lamberto, Elsie Ardelia","doi":"10.24198/jmi.v18.n1.38678.9-18","DOIUrl":"https://doi.org/10.24198/jmi.v18.n1.38678.9-18","url":null,"abstract":"When the insurance benefit of a last-survivor insurance product is payable at the moment of the last insured death, exploring continuous mortality models is essential to obtain the most appropriate premium and benefit reserve. In this study, Gamma-Gompertz mortality law was applied to Indonesian population mortality data at adulthood and old age stages to calculate the annual gross premium and gross benefit reserve of a whole life last survivor insurance product. The annual gross premium was computed using the actuarial equivalence principle. Results show that the older the policyholders purchase the product, the higher the annual gross premium they must pay. The gross benefit reserve needed to be set by the insurance company for the whole life last survivor insurance product was calculated using the prospective method. Its value grows for each valuation year until it approaches the insurance benefit amount.","PeriodicalId":53096,"journal":{"name":"Jurnal Matematika Integratif","volume":" ","pages":""},"PeriodicalIF":0.0,"publicationDate":"2022-05-23","publicationTypes":"Journal Article","fieldsOfStudy":null,"isOpenAccess":false,"openAccessPdf":"","citationCount":null,"resultStr":null,"platform":"Semanticscholar","paperid":"43877984","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 : 2022-05-23DOI: 10.24198/jmi.v18.n1.38343.27-39
Melina Melina, F. Sukono, Herlina Napitupulu, Valentina Adimurti Kusumaningtyas
To suppress the spread of COVID-19, almost all countries have been locked down. Most activities become work from home (WFH) so that triggers an increase in online transactions. Online transactions in-volving critical information require an electronic signature (DS), which is an authentication and verification tool. A fast and accurate pro-cess of sender legitimacy, authenticity, and anti-disclaimer is a must. The procedures used to prove the authenticity of DS, authenticity of the signer’s identity, and anti-repudiation can be carried out with authentication techniques. The purpose of this study is to propose a DS verification with an authentication technique based on system public-key cryptosystems by reversing the role of the private key and public key in the Rivest-Shamir-Adleman cryptographic algorithm. The electronic information attached to the DS will be stored in the message M, using a hash function against M to produce h = H ( M ) . The value of h will be encrypted to be a DS with the private key PR ( d, n ) . The signature is verified to prove its authenticity by decrypting the DS using the public key PU ( e, n ) , thus obtaining the value of h. The value of h is compared with the value of h (cid:48) which is obtained from the value of the message hash function M of the examined DS. If h = h (cid:48) means the DS is authentic. If the digit size is d > e , the signing time is longer than the time required for verification, and vice versa.
为了遏制新冠肺炎的传播，几乎所有国家都被封锁了。大多数活动变成了在家工作(WFH)，从而引发了在线交易的增加。涉及关键信息的在线交易需要电子签名(DS)，这是一种身份验证和验证工具。一个快速和准确的过程发件人的合法性，真实性和反免责声明是必须的。用于证明DS的真实性、签名者身份的真实性和反否认的程序可以通过身份验证技术来实现。本研究的目的是通过反转Rivest-Shamir-Adleman密码算法中私钥和公钥的作用，提出一种基于系统公钥密码系统的身份验证技术。附加到DS的电子信息将存储在消息M中，对M使用哈希函数生成h = h (M)。h的值将使用私钥PR (d, n)加密为DS。通过使用公钥PU (e, n)对DS进行解密，验证签名的真实性，从而得到h的值。将h的值与h (cid:48)的值进行比较，h的值是由被检查的DS的消息哈希函数M的值得到的。h = h (cid:48)表示DS是真实的。如果数字大小为d > e，则签名时间大于验证时间;反之，签名时间大于验证时间。
{"title":"Verifikasi Tanda Tangan Elektronik dengan Teknik Otentikasi Berbasis Kriptografi Kunci Publik Sistem Menggunakan Algoritma Kriptografi Rivest-Shamir-Adleman","authors":"Melina Melina, F. Sukono, Herlina Napitupulu, Valentina Adimurti Kusumaningtyas","doi":"10.24198/jmi.v18.n1.38343.27-39","DOIUrl":"https://doi.org/10.24198/jmi.v18.n1.38343.27-39","url":null,"abstract":"To suppress the spread of COVID-19, almost all countries have been locked down. Most activities become work from home (WFH) so that triggers an increase in online transactions. Online transactions in-volving critical information require an electronic signature (DS), which is an authentication and verification tool. A fast and accurate pro-cess of sender legitimacy, authenticity, and anti-disclaimer is a must. The procedures used to prove the authenticity of DS, authenticity of the signer’s identity, and anti-repudiation can be carried out with authentication techniques. The purpose of this study is to propose a DS verification with an authentication technique based on system public-key cryptosystems by reversing the role of the private key and public key in the Rivest-Shamir-Adleman cryptographic algorithm. The electronic information attached to the DS will be stored in the message M, using a hash function against M to produce h = H ( M ) . The value of h will be encrypted to be a DS with the private key PR ( d, n ) . The signature is verified to prove its authenticity by decrypting the DS using the public key PU ( e, n ) , thus obtaining the value of h. The value of h is compared with the value of h (cid:48) which is obtained from the value of the message hash function M of the examined DS. If h = h (cid:48) means the DS is authentic. If the digit size is d > e , the signing time is longer than the time required for verification, and vice versa.","PeriodicalId":53096,"journal":{"name":"Jurnal Matematika Integratif","volume":" ","pages":""},"PeriodicalIF":0.0,"publicationDate":"2022-05-23","publicationTypes":"Journal Article","fieldsOfStudy":null,"isOpenAccess":false,"openAccessPdf":"","citationCount":null,"resultStr":null,"platform":"Semanticscholar","paperid":"48422633","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 : 2022-05-23DOI: 10.24198/jmi.v18.n1.36585.1-8
Muhammad Audri Indraputra, Sanubari Tansah Tresna
The policy of importing goods has the possibility to become competitors of local products in the market. In general, people can choose to use local or imported products. Not infrequently people are more inclined to use imported products with consideration of brands and variations of choice. Of course, this competition has an impact on the absorption of local products by the community so that interventions need to be carried out to keep people from using local goods. In this paper, a determin-istic mathematical model is built to interpret the situation of users of imported and local goods by considering the number of imported and local products in the market and the influence of the role of the media in public education and persuasion efforts. Dynamical system theory is used to perform analysis on the model that has been built. The basic re-production ratio is determined to determine the absorption of imported products by the public. Then, numerical simulations are carried out to obtain predictions of the dynamics of users of imported and local goods by considering the implementation of the intervention.
{"title":"Analisis Dinamik Model Pengguna Barang Impor dan Lokal dengan Pengaruh Kebijakan dan Peran Media","authors":"Muhammad Audri Indraputra, Sanubari Tansah Tresna","doi":"10.24198/jmi.v18.n1.36585.1-8","DOIUrl":"https://doi.org/10.24198/jmi.v18.n1.36585.1-8","url":null,"abstract":"The policy of importing goods has the possibility to become competitors of local products in the market. In general, people can choose to use local or imported products. Not infrequently people are more inclined to use imported products with consideration of brands and variations of choice. Of course, this competition has an impact on the absorption of local products by the community so that interventions need to be carried out to keep people from using local goods. In this paper, a determin-istic mathematical model is built to interpret the situation of users of imported and local goods by considering the number of imported and local products in the market and the influence of the role of the media in public education and persuasion efforts. Dynamical system theory is used to perform analysis on the model that has been built. The basic re-production ratio is determined to determine the absorption of imported products by the public. Then, numerical simulations are carried out to obtain predictions of the dynamics of users of imported and local goods by considering the implementation of the intervention.","PeriodicalId":53096,"journal":{"name":"Jurnal Matematika Integratif","volume":" ","pages":""},"PeriodicalIF":0.0,"publicationDate":"2022-05-23","publicationTypes":"Journal Article","fieldsOfStudy":null,"isOpenAccess":false,"openAccessPdf":"","citationCount":null,"resultStr":null,"platform":"Semanticscholar","paperid":"42332509","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 : 2022-05-23DOI: 10.24198/jmi.v18.n1.36164.91-102
Valerie Valerie, H. Napitupulu, E. Carnia
The study of graph centrality in assessing the most central vertex in a graph or the most central or important individual in a network has been a prosperous field of exploration these days. Centrality observation in graphs is suitable for any graph with various kinds of centrality methods to be applied to many fields. In this study, simple, regular, directed and signed graph are being assessed by Degree, Eigenvector, and Beta Centrality. These three methods are related to each other; therefore, it is interesting to study the relation and the characteristic of each method. According to the result, Degree Centrality which assesses centrality based on vertexs direct links is applicable for every graph in this study. On the other hand, Eigenvector Centrality which asses a vertex centrality with respect to its neighbors centrality, is not applicable for the acyclic directed tree. While Beta Centrality is also advantageous for every graph in this study, the use of parameter β affects centrality scores depending on how the measure is conducted for local or global structure. Beta Centrality is an alternative to observing a vertexs centrality score by considering its direct links centrality, in the acyclic directed tree.
{"title":"Analisis Perbandingan Kesentralan Graf Dengan Degree, Eigenvector, dan Beta Centrality","authors":"Valerie Valerie, H. Napitupulu, E. Carnia","doi":"10.24198/jmi.v18.n1.36164.91-102","DOIUrl":"https://doi.org/10.24198/jmi.v18.n1.36164.91-102","url":null,"abstract":"The study of graph centrality in assessing the most central vertex in a graph or the most central or important individual in a network has been a prosperous field of exploration these days. Centrality observation in graphs is suitable for any graph with various kinds of centrality methods to be applied to many fields. In this study, simple, regular, directed and signed graph are being assessed by Degree, Eigenvector, and Beta Centrality. These three methods are related to each other; therefore, it is interesting to study the relation and the characteristic of each method. According to the result, Degree Centrality which assesses centrality based on vertexs direct links is applicable for every graph in this study. On the other hand, Eigenvector Centrality which asses a vertex centrality with respect to its neighbors centrality, is not applicable for the acyclic directed tree. While Beta Centrality is also advantageous for every graph in this study, the use of parameter β affects centrality scores depending on how the measure is conducted for local or global structure. Beta Centrality is an alternative to observing a vertexs centrality score by considering its direct links centrality, in the acyclic directed tree.","PeriodicalId":53096,"journal":{"name":"Jurnal Matematika Integratif","volume":" ","pages":""},"PeriodicalIF":0.0,"publicationDate":"2022-05-23","publicationTypes":"Journal Article","fieldsOfStudy":null,"isOpenAccess":false,"openAccessPdf":"","citationCount":null,"resultStr":null,"platform":"Semanticscholar","paperid":"43194401","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 : 2022-05-23DOI: 10.24198/jmi.v18.n1.37640.81-90
Yunita Septriana Anwar, I. Wijayanti, Budi Surodjo, Dewi Kartika Sari
A pullback of two morphisms with a common codomain f : A → C and g : B → C is the limit of a diagram consisting f and g . The dual notion of a pullback is called a pushout. A Pullback of morphisms f : A → C and g : B → C in R-MOD is a diagram that contains Ker ( p ∗ ) = { ( a, b ) ∈ A (cid:76) B | f ( a ) = g ( b ) } ⊂ A (cid:76) B where p ∗ = fπ 1 − gπ 2 : A (cid:76) B → C , and a pushout of morphisms k : A → B and l : A → C in R-MOD is a diagram that contains Coke ( q ∗ ) = B ⊕ C/Im ( q ∗ ) where q ∗ = ε 1 k + ε 2 l : A → B ⊕ C . In this paper, we inves-tigate existence of pullback and pushout in TopR-MOD as a subcategory of R-MOD by giving product topology τ prod on pullback and coproduct topology τ coprod on pushout. Furthermore, a pullback of two continuous homomorphisms f : A → C and g : B → C in TopR-MOD is a diagram that contains A × C B = { ( a, b ) ∈ A × B | f ( a ) = g ( b ) } ⊂ A × B with the subspace topology of τ prod on A × C B , and the pushout of two continuous homomorphisms k : A → B and l : A → C in TopR-MOD is a diagram that contains B (cid:76) A C = ( B (cid:76) C ) / ∼ where ∼ is the smallest equivalence relation containing the pairs ( k ( a ) , l ( a )) for all a ∈ A and topology on B (cid:76) C is coproduct topology τ coprod .
{"title":"Pullback dan Pushout di Kategori Modul Topologis","authors":"Yunita Septriana Anwar, I. Wijayanti, Budi Surodjo, Dewi Kartika Sari","doi":"10.24198/jmi.v18.n1.37640.81-90","DOIUrl":"https://doi.org/10.24198/jmi.v18.n1.37640.81-90","url":null,"abstract":"A pullback of two morphisms with a common codomain f : A → C and g : B → C is the limit of a diagram consisting f and g . The dual notion of a pullback is called a pushout. A Pullback of morphisms f : A → C and g : B → C in R-MOD is a diagram that contains Ker ( p ∗ ) = { ( a, b ) ∈ A (cid:76) B | f ( a ) = g ( b ) } ⊂ A (cid:76) B where p ∗ = fπ 1 − gπ 2 : A (cid:76) B → C , and a pushout of morphisms k : A → B and l : A → C in R-MOD is a diagram that contains Coke ( q ∗ ) = B ⊕ C/Im ( q ∗ ) where q ∗ = ε 1 k + ε 2 l : A → B ⊕ C . In this paper, we inves-tigate existence of pullback and pushout in TopR-MOD as a subcategory of R-MOD by giving product topology τ prod on pullback and coproduct topology τ coprod on pushout. Furthermore, a pullback of two continuous homomorphisms f : A → C and g : B → C in TopR-MOD is a diagram that contains A × C B = { ( a, b ) ∈ A × B | f ( a ) = g ( b ) } ⊂ A × B with the subspace topology of τ prod on A × C B , and the pushout of two continuous homomorphisms k : A → B and l : A → C in TopR-MOD is a diagram that contains B (cid:76) A C = ( B (cid:76) C ) / ∼ where ∼ is the smallest equivalence relation containing the pairs ( k ( a ) , l ( a )) for all a ∈ A and topology on B (cid:76) C is coproduct topology τ coprod .","PeriodicalId":53096,"journal":{"name":"Jurnal Matematika Integratif","volume":" ","pages":""},"PeriodicalIF":0.0,"publicationDate":"2022-05-23","publicationTypes":"Journal Article","fieldsOfStudy":null,"isOpenAccess":false,"openAccessPdf":"","citationCount":null,"resultStr":null,"platform":"Semanticscholar","paperid":"47709517","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 : 2022-05-23DOI: 10.24198/jmi.v18.n1.38478.41-51
Yolwi Dyatma, I. G. P. Purnaba, H. Sumarno
{"title":"Cadangan Manfaat Minimum dan Maksimum Asuransi Jiwa Seumur Hidup dan Berjangka dengan Metode Prospektif","authors":"Yolwi Dyatma, I. G. P. Purnaba, H. Sumarno","doi":"10.24198/jmi.v18.n1.38478.41-51","DOIUrl":"https://doi.org/10.24198/jmi.v18.n1.38478.41-51","url":null,"abstract":"","PeriodicalId":53096,"journal":{"name":"Jurnal Matematika Integratif","volume":" ","pages":""},"PeriodicalIF":0.0,"publicationDate":"2022-05-23","publicationTypes":"Journal Article","fieldsOfStudy":null,"isOpenAccess":false,"openAccessPdf":"","citationCount":null,"resultStr":null,"platform":"Semanticscholar","paperid":"44266607","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}
The locating chromatic number of a graph extends the partition dimension and vertex coloring of a graph. The minimum number of locating coloring of graph G is called the locating chromatic number of graph G . This paper will discuss the locating chromatic number of path split graph and barbell path split graph. The method used to obtain the locating chromatic number of the graph is to determine the upper and lower bound. The results obtained are that the path split graph’s locating chromatic number and the barbell are the same, namely 4.
{"title":"Bilangan Kromatik Lokasi Graf Split Lintasan","authors":"Siti Rahmatalia, Asmiati Asmiati, Notiragayu Notiragayu","doi":"10.24198/jmi.v18.n1.36091.73-80","DOIUrl":"https://doi.org/10.24198/jmi.v18.n1.36091.73-80","url":null,"abstract":"The locating chromatic number of a graph extends the partition dimension and vertex coloring of a graph. The minimum number of locating coloring of graph G is called the locating chromatic number of graph G . This paper will discuss the locating chromatic number of path split graph and barbell path split graph. The method used to obtain the locating chromatic number of the graph is to determine the upper and lower bound. The results obtained are that the path split graph’s locating chromatic number and the barbell are the same, namely 4.","PeriodicalId":53096,"journal":{"name":"Jurnal Matematika Integratif","volume":" ","pages":""},"PeriodicalIF":0.0,"publicationDate":"2022-05-23","publicationTypes":"Journal Article","fieldsOfStudy":null,"isOpenAccess":false,"openAccessPdf":"","citationCount":null,"resultStr":null,"platform":"Semanticscholar","paperid":"49063898","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 : 2022-05-23DOI: 10.24198/jmi.v18.n1.35796.53-62
Alma Justica, Sandra Kezia, David Eurico, Alif Anindyanari Putri Priyambudi, Ratu Alivya Syahrazard Anees, Achmad Zanbar Soleh
Reserves are crucial for insurance companies because it is used to avoid unexpected risk such as unexpected claims and others. Insurance companies are required to have premium reserves and be able to manage them properly in order to cope with future claims by policyholder. There-fore, it is important for insurance companies to calculate reserves. To calculate reserves, insurance companies use a tool in the form of an application. Based on a survey conducted at 2019 Indonesian Actuaries Summit, there are 23% of insurance companies in Indonesia that still use conventional applications because the price offered to buy the more modern application such as Prophet is quite expensive. Meanwhile, the use of conventional application requires a relatively longer time with a higher probability of error in calculating reserves. Therefore, an application program for calculating insurance reserves is needed that can complete calculations more effectively, cheaply, and easily. This study designed GPV Reserve application using the Python programming lan-guage to calculate reserves for endowment life insurance using the Gross Premium Valuation (GPV) model approach. This application can be a tool for life insurance companies in calculating insurance reserves, es-pecially with endowment life insurance products.
{"title":"Perhitungan Cadangan Asuransi Tahunan dengan Metode Gross Premium Valuation menggunakan Bahasa Pemrograman Python","authors":"Alma Justica, Sandra Kezia, David Eurico, Alif Anindyanari Putri Priyambudi, Ratu Alivya Syahrazard Anees, Achmad Zanbar Soleh","doi":"10.24198/jmi.v18.n1.35796.53-62","DOIUrl":"https://doi.org/10.24198/jmi.v18.n1.35796.53-62","url":null,"abstract":"Reserves are crucial for insurance companies because it is used to avoid unexpected risk such as unexpected claims and others. Insurance companies are required to have premium reserves and be able to manage them properly in order to cope with future claims by policyholder. There-fore, it is important for insurance companies to calculate reserves. To calculate reserves, insurance companies use a tool in the form of an application. Based on a survey conducted at 2019 Indonesian Actuaries Summit, there are 23% of insurance companies in Indonesia that still use conventional applications because the price offered to buy the more modern application such as Prophet is quite expensive. Meanwhile, the use of conventional application requires a relatively longer time with a higher probability of error in calculating reserves. Therefore, an application program for calculating insurance reserves is needed that can complete calculations more effectively, cheaply, and easily. This study designed GPV Reserve application using the Python programming lan-guage to calculate reserves for endowment life insurance using the Gross Premium Valuation (GPV) model approach. This application can be a tool for life insurance companies in calculating insurance reserves, es-pecially with endowment life insurance products.","PeriodicalId":53096,"journal":{"name":"Jurnal Matematika Integratif","volume":" ","pages":""},"PeriodicalIF":0.0,"publicationDate":"2022-05-23","publicationTypes":"Journal Article","fieldsOfStudy":null,"isOpenAccess":false,"openAccessPdf":"","citationCount":null,"resultStr":null,"platform":"Semanticscholar","paperid":"47606497","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}
Parameters of a distribution are usually unknown values, to find out an estimate is made of these parameters. There are two kinds of parameter estimation methods, namely classical method and Bayesian method. Bayesian method was a method that combines sample distribution with prior distribution. To get a random sample is to use a simulation. One of the simulation techniques used in Bayesian method is Markov Chain Monte Carlo (MCMC) method, which is a simulation method for generating random variables based on the Markov chain. This study discusses Bayesian method with MCMC using Gibbs Sampling algorithm. MCMC method with Gibbs Sampling algorithm works to build a Markov chain by recursively sampling from full conditional posterior distribution of each parameter. In this study, Bayesian method with MCMC using Gibbs Sampling algorithm was applied to estimate parameters of the Stochastic Volatility to converge. Stochastic volatility is a concept that allows for the fact that asset price volatility varies over time and is not constant. This model applied for predicting stock returns of PT. Indofood CBP Sukses Makmur Tbk. (ICBP.JK). Based on Stochastic Volatility model obtained, prediction results for stock returns are almost close to the actual data. Benefit of this research is that the predicted value obtained can be used as a reference for investors to create an optimal portfolio.
分布的参数通常是未知值，要找出这些参数的估计值。参数估计方法有两种，即经典方法和贝叶斯方法。贝叶斯方法是一种将样本分布与先验分布相结合的方法。要获得随机样本，就要使用模拟。贝叶斯方法中使用的模拟技术之一是马尔可夫链蒙特卡罗（MCMC）方法，这是一种基于马尔可夫链生成随机变量的模拟方法。本研究使用吉布斯采样算法讨论了MCMC的贝叶斯方法。MCMC方法结合吉布斯采样算法，通过对每个参数的全条件后验分布进行递归采样，建立马尔可夫链。在本研究中，将贝叶斯方法和MCMC结合使用吉布斯抽样算法来估计随机波动率的参数以收敛。随机波动率是一个概念，考虑到资产价格波动率随时间变化而不是恒定的。该模型应用于印尼食品公司CBP Sukses Makmur Tbk的股票收益预测。（ICBP.JK）。基于随机波动率模型，股票收益率的预测结果与实际数据基本接近。这项研究的好处是，获得的预测值可以作为投资者创建最佳投资组合的参考。
{"title":"Estimasi Parameter Model Volatilitas Stokastik dengan Metode Bayesian Rantai Markov Monte Carlo untuk Memprediksi Return Saham","authors":"Rahmayanti Putri Desiresta, Firdaniza Firdaniza, Kankan Parmikanti","doi":"10.24198/jmi.v17.n2.34805.73-83","DOIUrl":"https://doi.org/10.24198/jmi.v17.n2.34805.73-83","url":null,"abstract":"Parameters of a distribution are usually unknown values, to find out an estimate is made of these parameters. There are two kinds of parameter estimation methods, namely classical method and Bayesian method. Bayesian method was a method that combines sample distribution with prior distribution. To get a random sample is to use a simulation. One of the simulation techniques used in Bayesian method is Markov Chain Monte Carlo (MCMC) method, which is a simulation method for generating random variables based on the Markov chain. This study discusses Bayesian method with MCMC using Gibbs Sampling algorithm. MCMC method with Gibbs Sampling algorithm works to build a Markov chain by recursively sampling from full conditional posterior distribution of each parameter. In this study, Bayesian method with MCMC using Gibbs Sampling algorithm was applied to estimate parameters of the Stochastic Volatility to converge. Stochastic volatility is a concept that allows for the fact that asset price volatility varies over time and is not constant. This model applied for predicting stock returns of PT. Indofood CBP Sukses Makmur Tbk. (ICBP.JK). Based on Stochastic Volatility model obtained, prediction results for stock returns are almost close to the actual data. Benefit of this research is that the predicted value obtained can be used as a reference for investors to create an optimal portfolio.","PeriodicalId":53096,"journal":{"name":"Jurnal Matematika Integratif","volume":" ","pages":""},"PeriodicalIF":0.0,"publicationDate":"2022-01-23","publicationTypes":"Journal Article","fieldsOfStudy":null,"isOpenAccess":false,"openAccessPdf":"","citationCount":null,"resultStr":null,"platform":"Semanticscholar","paperid":"47883862","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 : 2022-01-23DOI: 10.24198/jmi.v17.n2.34646.119-126
A. Faisol, F. Fitriani
Diberikan sebarang ring komutatif $R$ dengan elemen satuan, monoid terurut tegas $(S,leq)$, homomorfisma monoid $omega:Srightarrow End(R)$, submonoid $S_1,S_2subseteq S$ yang masing-masing dilengkapi urutan $leq_1, leq_2$ yang textit{coarser} terhadap urutan $leq$ pada $S$, dan modul $M_1,M_2$ atas $R$. Pada penelitian ini, dikonstruksi modul deret pangkat tergeneralisasi miring $M_1[[S_1,leq_1,omega]]$ dan $M_2[[S_2,leq_2,omega]]$ atas ring deret pangkat tergeneralisasi miring $R[[S,leq,omega]]$. Selain itu, dibuktikan pemetaan $tau$ dari $M_1[[S_1,leq_1,omega]]$ ke $M_2[[S_2,leq_2,omega]]$ dengan $tau(alpha_1)=gammacircalpha_1circdelta^{-1}$ merupakan $R[[S,leq,omega]]$-homomorfisma modul dengan mensyaratkan $f(delta^{-1}(u))=f(u)$ dan $omega_{delta^{-1}(v)}=omega_{v}$ untuk setiap $u,vin S_2$ dan $fin R[[S,leq,omega]]$.
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