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All Journal Journal of the Indonesian Mathematical Society BAREKENG: Jurnal Ilmu Matematika dan Terapan Communication in Biomathematical Sciences
Pasaribu, Udjianna Sekteria
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Computer Science & IT Control & Systems Engineering Economics, Econometrics & Finance Energy Engineering Mathematics Mechanical Engineering Physics Social Sciences Transportation

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Joint-Life Insurance Premium Model Using Archimedean Copula: The Study of Mortality in Indonesia Ramadhan, Muhammad Akhirul; Zainuddin, Ahmad Fuad; Pasaribu, Udjianna Sekteria; Sari, RR Kurnia Novita
Journal of the Indonesian Mathematical Society Vol. 31 No. 1 (2025): MARCH
Publisher : IndoMS

Show Abstract | Download Original | Original Source | Check in Google Scholar | DOI: 10.22342/jims.v31i1.1783

Abstract

Joint-life insurance pays a sum insured when the first death occurs. This insurance has a case based on the order of exit from the cohort, namely joint life and last survivor. The former means that one of the insured leaves the cohort, while the latter means the last member of the insured has left his or her cohort. For some reasons of simplicity, the insurance premium is usually calculated with the assumption that the husband and wife are mutually independent. However, this assumption is considered unrealistic. Couples are open to the same risks, hence explaining joint survival model should involve dependence structures between the distribution of spouse mortality. In line with this, to understand the dependence structure of multiple random variables, the approach used is Copula. In this context, Copula relates the marginal distribution function of these variables to the joint life distribution. One of the advantages from Copula is that the random variables do not have to come from the same distribution, hence Copula is considered good enough to explain the dependence of the mortality rate between husband and wife. This study aimed to develop a joint survival model for calculating joint life insurance premiums using the concept of Archimedean Copula to discover the minimum premium value by conducting the following steps: first, identifying the marginal distributions of mortality for genders using Indonesian Mortality Table IV (TMI/Tabel Mortalitas Indonesia IV); second, Archimedean copula function-based constructing survival models that captures the relationship between these variables; third, setting dependency parameter θ; fourth, calculating the joint life premium using Archimedean copula based survival modeled for each correlation dependency level; and carrying out optimization to find the minimum premium value. This can be achieved by formulating the problem as an optimization problem, considering an objective function that yields the lowest premium till satisfying the financial requirements of the insurance company.
K-MEANS AND AGGLOMERATIVE HIERARCHY CLUSTERING ANALYSIS ON THE STAINLESS STEEL CORROSION PROBLEM Afrianti, Yuli Sri; Pasaribu, Udjianna Sekteria; Sulaiman, Fadhil Hanif; Angelia, Grace; Wattimanela, Henry Junus
BAREKENG: Jurnal Ilmu Matematika dan Terapan Vol 18 No 1 (2024): BAREKENG: Journal of Mathematics and Its Application
Publisher : PATTIMURA UNIVERSITY

Show Abstract | Download Original | Original Source | Check in Google Scholar | DOI: 10.30598/barekengvol18iss1pp0589-0602

Abstract

Stainless Steel (SS) is a material that is widely used in various fields because it is resistant to corrosion. However, if SS is exposed to heat at high temperatures for a long period of time, a sigma phase, namely the Fe-Cr compound, will form, which indicates that corrosion has begun. The appearance of this corrosion can be detected through color changes on the SS surface, ranging from light brown to dark blue. Corrosion events will be observed through the distribution of color on the sample surface at the location selected through the SS microstructure image. Cluster analysis will be used to group the colors on the surface of the SS sample through the images used. The results of cluster analysis can be used to identify SS color which indicates the appearance of corrosion in the sample. In this research, we will examine the determination of many clusters for K-Means and Agglomerative Hierarchy with Ward's Criterion, Single, Average, and Complete Linkages. In addition, the model quality measure was tested with Silhouette Coeficient. Single linkage gives the worst results because it gives the impression that only one dominant color appears so it can be said that it is unable to distribute each color to the specified cluster. Likewise with Average because the number of clusters cannot be determined with certainty. On the other hand, the K-Means results are similar to Ward's results, this is reasonable because the basic idea of both is to find the minimum distance between each object and its center, in this case the average is used as the measure of the center, while the results that are most similar to the original image are clustering uses complete linkage. These results can be used as recommendations for academics and practitioners in the fields of Statistics, Mathematics and Materials Engineering in the subsequent analysis process to solve SS corrosion problems.
MODELING CUSTOMER LIFETIME VALUE WITH MARKOV CHAIN IN THE INSURANCE INDUSTRY Mahdiyasa, Adilan Widyawan; Pasaribu, Udjianna Sekteria; Sari, Kurnia Novita
BAREKENG: Jurnal Ilmu Matematika dan Terapan Vol 19 No 1 (2025): BAREKENG: Journal of Mathematics and Its Application
Publisher : PATTIMURA UNIVERSITY

Show Abstract | Download Original | Original Source | Check in Google Scholar | DOI: 10.30598/barekengvol19iss1pp687-696

Abstract

In the competitive insurance industry, accurately predicting Customer Lifetime Value (CLV) is vital for sustaining long-term profitability and optimizing resource allocation. Traditional static models often fail to capture the dynamic and uncertain nature of customer behavior, which is influenced by factors such as life changes, economic conditions, and evolving product offerings. To address these limitations, this paper proposes an advanced modeling approach that integrates Markov Chains with survival analysis. Markov Chains are well-suited for modeling stochastic processes, where future states depend on current conditions, while survival analysis provides insights into event timing and likelihood for estimating the insurance premium. The proposed model combines these approaches to make a more complete and accurate prediction of CLV. This helps insurers make better decisions and improves the overall performance of their business. We employ the data of customer behavior from the insurance company in Bandung, Indonesia from 1994 to 2020. We found that CLV in the insurance industry is significantly affected by customer behavior.
Linear Mixed Model for Oil Palm Parents Selection Sonhaji, Abdullah; Pasaribu, Udjianna Sekteria; Indratno, Sapto Wahyu; Pancoro, Adi
Communication in Biomathematical Sciences Vol. 8 No. 1 (2025)
Publisher : The Indonesian Bio-Mathematical Society

Show Abstract | Download Original | Original Source | Check in Google Scholar | DOI: 10.5614/cbms.2025.8.1.3

Abstract

The objective of plant breeding is to obtain superior seeds. These seeds originated from parents that can pass their superior traits to their progeny. The observed characteristics of the progeny (phenotype) determined the traits of these seeds. Therefore, we performed a progeny analysis. In this analysis, the data samples were collected from Riau in Sumatera and Kumai in Kalimantan (two locations). The main objective is to find superior parents from these two locations. The superiority of the selected parents lies not only in passing high production traits but also in adaptability (fit) to the diversity or variability of the environment or locations. This analysis calculates the General Combining Ability (GCA) values for both male and female parents using the Linear Mixed Model (LMM). The experimental design, as the source of data, was an alpha lattice design, so the LMM contains locations, replicas, blocks, male and female parents, and the progeny factors. The analyzed phenotype is Fresh Fruit Bunches of third-year production. Since the data sets of the two locations were nonintersect, the model uses the coefficient of parentage (additive relationship matrix) to link both. The results of the GCA analysis showed that selected female parents were 137, 155, 126, 147, and 159 (Dura), and 101, 113, 109, and 117 for male parents. They are among the parents with highly productive progenies. There are also new potential crossings not currently available on the plantation - for example, the crossing 137 x 101 with the additive genetic value of 35.37.
Co-Authors Adi Pancoro Afrianti, Yuli Sri Angelia, Grace Indratno, Sapto Wahyu KURNIA NOVITA SARI Mahdiyasa, Adilan Widyawan Ramadhan, Muhammad Akhirul Sari, RR Kurnia Novita Sonhaji, Abdullah Sulaiman, Fadhil Hanif Wattimanela, Henry Junus Zainuddin, Ahmad Fuad