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All Journal Statistika BAREKENG: Jurnal Ilmu Matematika dan Terapan
Dumaria R. Tampubolon
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Computer Science & IT Control & Systems Engineering Decision Sciences, Operations Research & Management Economics, Econometrics & Finance Energy Engineering Industrial & Manufacturing Engineering Mathematics Mechanical Engineering Physics Transportation

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Run-Off Triangle Data dan Permasalahannya Aceng Komarudin Mutaqin; Dumaria R. Tampubolon; Sutawanir Darwis
STATISTIKA: Forum Teori dan Aplikasi Statistika Vol 8, No 1 (2008)
Publisher : Program Studi Statistika Unisba

Show Abstract | Download Original | Original Source | Check in Google Scholar | DOI: 10.29313/jstat.v8i1.975

Abstract

Run-off triangle data sering digunakan sebagai dasar untuk menaksir cadangan kerugian dari suatuperusahaan asuransi umum kelas bisnis long-tail. Run-off triangle data memuat gambaran klaimkeseluruhan (aggregate), dan merupakan ringkasan dari suatu data set klaim-klaim individu.Makalah ini mengupas run-off triangle data tersebut bersama-sama dengan permasalahan yang adadi dalamnya. Dalam makalah ini dikemukakan dua masalah, yaitu pertama untuk kasus-kasustertentu, tidak semua data dalam run-off triangle teramati. Kemudian masalah yang kedua adalahadanya nilai-nilai incremental data yang negatif dalam run-off triangle terutama dalam incurred claimsdata.
A MODEL ON MARKET EQUILIBRIUM USING A DIFFERENTIAL EQUATION WITH TIME DELAYS Widjaja, Jalina; Putra Irawan, Naufal Zidan; Soeharyadi, Yudi; Tampubolon, Dumaria R.
BAREKENG: Jurnal Ilmu Matematika dan Terapan Vol 19 No 3 (2025): BAREKENG: Journal of Mathematics and Its Application
Publisher : PATTIMURA UNIVERSITY

Show Abstract | Download Original | Original Source | Check in Google Scholar | DOI: 10.30598/barekengvol19iss3pp1893-1904

Abstract

In this paper, a model on market equilibrium is proposed using a delay differential equation with discrete delays as a modified version of the one proposed by Kobayashi (1996). The price of a commodity is determined using the equation involving weighted supply and demand functions. Both supply and demand functions are considered at the current time and sometimes in the past. The delays are chosen by considering the seasonal behavior of the market. We use data on some main commodities in Indonesia from 2018 to 2024 to validate the model. We found that the implementation of our modified Kobayashi model improves the estimation given by the original one. The implementation of the method also shows some characteristics of delay equations, that is longer delay time may include more dynamics, and more fluctuation, although that means it is more prone to instabilities. However, the problem of optimal delay time is yet to be resolved.
Co-Authors Aceng Komarudin Mutaqin Putra Irawan, Naufal Zidan Sutawanir Darwis Widjaja, Jalina Yudi Soeharyadi