SEBARAN STASIONER PADA SISTEM BONUS-MALUS SWISS SERTA MODIFIKASINYA (Stationary Distribution of Swiss Bonus-Malus System and its Modification)

Authors

  • Cherry Galatia Ballangan Faculty of Industrial Engineering, Petra Christian University
  • Hadi Sumarno Fakultas Matematika & IPA, Jurusan Matematika, Institut Pertanian Bogor

:

https://doi.org/10.9744/informatika.3.2.pp.%2097-103

Keywords:

stationary distrubution, resursive formula, Swiss Bonus-Malus System.

Abstract

Bonus-Malus System is a system in actuary that introduce the premium class (state) partition, where the state is influenced by the number of annual claims reported by the policy holder. We could base the determination of the state on the stationary distribution that represent the number of policy holders in any state. Swiss Bonus-Malus System has 22 state. The number of state that involved in this system result in the difficulty of stationary distribution determination. Therefore, the aim of this paper is to study a method to obtain stationary distribution of Swiss Bonus-Malus System by recursive formula, with this recursive formula, the stationary distribution of Swiss Bonus-Malus System can be determined easier. Modification of this system with infinite state result in the changes of recursive formula to obtain the stationary. This changes including the determining of base value of the recursive formula. Abstract in Bahasa Indonesia : Sistem Bonus-Malus merupakan sistem dalam aktuaria yang memperkenalkan pembagian kelas premi (state) yang dipengaruhi oleh jumlah klaim yang diajukan oleh pemegang polis tiap tahunnya. Penetapan state dalam sistem ini didasarkan pada pencarian sebaran stasioner yang menyatakan banyaknya pemegang polis dalam tiap state. Sistem Bonus-Malus Swiss (BMS) memiliki 22 state. Banyaknya state yang terlibat dalam sistem ini mengakibatkan sulitnya penentuan sebaran stasioner pada sistem BMS tersebut. Karena itu dalam tulisan ini dipelajari suatu metode penentuan sebaran stasioner dari sistem BMS tersebut, yaitu dengan menggunakan formula rekursif. Dengan formula rekursif ini, sebaran stasioner sistem BMS dapat ditentukan dengan mudah. Modifikasi sistem BMS untuk jumlah state yang tak hingga mengakibatkan perubahan pada formula rekursif untuk mencari sebaran stasionernya. Perubahan ini meliputi penetapan nilai awal dari formula rekursif tersebut. Kata kunci: sebaran stasioner, formula rekursif, sistem Monus-Malus Swiss.

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Published

2004-06-21

How to Cite

Ballangan, C. G., & Sumarno, H. (2004). SEBARAN STASIONER PADA SISTEM BONUS-MALUS SWISS SERTA MODIFIKASINYA (Stationary Distribution of Swiss Bonus-Malus System and its Modification). Jurnal Informatika, 3(2), pp. 97-103. https://doi.org/10.9744/informatika.3.2.pp. 97-103

Issue

Vol. 3 No. 2 (2002): NOVEMBER 2002

Section

Articles

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