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All Journal Epsilon: Jurnal Matematika Murni dan Terapan
Aprida Siska Lestia
Program Studi Matematika FMIPA ULM
Decision Sciences, Operations Research & Management Transportation

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UKURAN RISIKO ATAS PERTANGGUNGAN DENGAN BESAR KLAIM YANG TERMODIFIKASI Aprida Siska Lestia
EPSILON: JURNAL MATEMATIKA MURNI DAN TERAPAN Vol 17, No 1 (2023)
Publisher : Mathematics Study Program, Faculty of Mathematics and Natural Sciences, Lambung Mangkurat

Show Abstract | Download Original | Original Source | Check in Google Scholar | DOI: 10.20527/epsilon.v17i1.9051

Abstract

Coverage modifications results in the amount of payment or reimbursement of claims not being the same as that proposed by the policyholder. Determination of the deductible causes claims below that value to be borne by the policyholder. Meanwhile, setting a policy limit results in a maximum value for claims borne by the insurance company (maximum covered loss). The size of risk as an important value in risk management, which in its determination depends on the distribution of losses in the form of claims, will also be affected by coverage modifications. In this study, risk measure was determined based on the standard deviation and value at risk that using quantile values. In addition, a risk measure is also determined in the form of a conditional tail expectation which is the average value of the loss over a certain quantile and the risk measure is based on a proportional hazard transformation. The size of the risk is determined by the coverage modified by the deductible and policy limit. Apart from that, it is also taken into account that there may be inflation, which of course will also have an impact on the distribution of claims. The observed claim size is known to have a Weibull distribution with certain parameter values, which heavy tailed. The results obtained indicate that modifications in the form of setting deductibles and policy limits have an impact on the magnitude of all risk measures obtained.
MODEL MATEMATIKA PENYEBARAN KONSTITUEN DALAM PEMILIHAN UMUM PRESIDEN DENGAN ADANYA MEDIA MASSA Muhammad Anshar; Faisal Faisal; Aprida Siska Lestia
EPSILON: JURNAL MATEMATIKA MURNI DAN TERAPAN Vol 17, No 2 (2023)
Publisher : Mathematics Study Program, Faculty of Mathematics and Natural Sciences, Lambung Mangkurat

Show Abstract | Download Original | Original Source | Check in Google Scholar | DOI: 10.20527/epsilon.v17i2.10146

Abstract

The presidential election is the process of selecting people to fill the presidency, in Indonesia direct presidential elections have been held since 2014. The popularity of a candidate is affected by exposure of news from the mass media. News from the mass media can spread from one individual or group to another, thus it can influence the behavior of a constituent, and an epidemiological model can be used. The purpose of this research was to explain the formation of the model, determine the equilibrium point, analyze the stability at the equilibrium point, performing a simulation, and determine the numerical solution. This research was carried out firstly by making the assumptions used in the formation of the model, then determining the equilibrium point of the model. After that, the stability of the equilibrium point will be analyzed by linearizing the model so that the Jacobian matrix was obtained, determining the eigenvalues of the Jacobian matrix, performing a simulation, and determine the numerical solution using the parameters of the 2014 presidential election results and with the fifth order Runge-Kutta method. The result of this study was the formation of two a mathematical model for the distribution of constituents in the presidential election with the existence of mass media, namely when the proportion of constituents affected by positive news is zero and non-zero. Based on this model when the proportion of constituents affected by positive news is zero, two equilibrium points were obtained, namely the equilibrium point free of constituents supporting political figures () and the equilibrium point of constituents supporting political figures (). Then, based on the model when the proportion of constituents affected by positive news is non-zero, the equilibrium point of the political figure supporting constituents () is obtained. From the stability analysis of the equilibrium point  and equilibrium point , local asymptotic stability was obtained, and from the numerical simulations, it was obtained that the difference in the vote acquisition.
Co-Authors Faisal Faisal Muhammad Anshar