Stochastic Interest Model Based on Compound Poisson Process and Applications in Actuarial Science

Li, Shilong; Yin, Chuancun; Zhao, Xin; Dai, Hongshuai

doi:10.1155/2017/3472319

Cited by 4 publications

(3 citation statements)

References 22 publications

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“…In queuing theory, it appears naturally in batch arriving queue models [9,Chapter 6]. In actuarial finance, it comes forth both in ruin theory as a part of the Crameŕ-Lundberg process and its generalizations, see [5,Chapter 4], as well as in stochastic interest modelling [10].…”

Section: Introductionmentioning

confidence: 99%

The Bell-Touchard Counting process

Rodríguez¹

2022

Preprint

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The Poisson process is one of the simplest stochastic processes defined in continuous time, having interesting mathematical properties, leading, in many situations, to applications mathematically treatable. One of the limitations of the Poisson process is the rare events hypothesis; which is the hypothesis of unitary jumps within an infinitesimal window of time. Although that restriction may be avoided by the compound Poisson process, in most situations, we don't have a closed expression for the probability distribution of the increments of such processes, leaving us options such as working with probability generating functions, numerical analysis and simulations. It is with this motivation in mind, inspired by the recent developments of discrete distributions, that we propose a new counting process based on the Bell-Touchard probability distribution, naming it the Bell-Touchard process. We verify that the process is a compound Poisson process, a multiple Poisson process and that it is closed for convolution plus decomposition operations. Besides, we show that the Bell-Touchard process arises naturally from the composition of two Poisson processes. Moreover, we propose two generalizations; namely, the compound Bell-Touchard process and the non-homogeneous Bell-Touchard process, showing that the last one arises from the composition of a non-homogeneous Poisson process along with a homogeneous Poisson process. We emphasize that since previous works have been shown that the Bell-Touchard probability distribution can be used quite effectively for modelling count data, the Bell-Touchard process and its generalizations may contribute to the formulation of mathematical treatable models where the rare events hypothesis is not suitable.

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Section: Introductionmentioning

confidence: 99%

The Bell-Touchard Counting process

Rodríguez¹

2022

Preprint

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“…Many topics based on the web renewal risk process shall be investigated. For example, Li et al [ 16 ] studied a stochastic interest model based on compound Poisson process, and it is of interest to study the problem based on the web renewal risk process.…”

Section: Discussionmentioning

confidence: 99%

Web renewal counting processes and their applications in insurance

Zhang

2018

J Inequal Appl

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“…). Pada perhitungan anuitas jiwa kontinu untuk asuransi jiwa menggunkan life table dengan asumsi uniform, terlihat semakin meningkatnya suku bunga menyebabkan nilai APV semakin rendah(Lie et al, 2017). Nilai APV merupakan nilai sekarang untuk nilai polis dari pembayaran manfaat.…”

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Sukraini¹,

Elfarosa²

2018

JMBK

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Tujuan dari penelitian ini adalah mencari nilai premi asuransi jiwa kredit menggunakan konsep aktuaria pada asuransi jiwa berjangka. Objek penelitian adalah premi pada lembaga keuangan mikro yaitu koperasi dan Lembaga Perkreditan Rakyat (LPD). Premi pada konsep aktuaria memperhitungkan mortalita berdasarkan usia dan jenis kelamin, dan tingkat bunga yang ditetapkan yaitu mengacu pada BI rate sebesar 6,5%. Hasil analisis perhitungan menunjukan, semakin tinggi usia debitur berdasarkan perhitungan aktuaria nilai premi akan semakin tinggi, begitupula dengan premi yang berlaku pada LPD Desa Adat Pecatu namun berbeda halnya dengan premi pada Koperasi Pegawai Negeri Politeknik Negeri Bali (KPN PNB). Premi pada KPN PNB hanya berdasarkan jangka waktu pinjaman saja sehingga nilai premi akan sama untuk semua usia. Hasil perhitungan aktuaria menunjukkan semakin tinggi usia, peluang kematian semakin meningkat. Golongan perempuan dianggap mempunyai risiko asuransi yang lebih baik daripada laki-laki. Kata kunci: asuransi jiwa kredit, asuransi jiwa berjangka, premi tunggal bersih, mortalita, actuarial present value. ABTRACT The purpose of this study is to find the value of life insurance credit premiums using the actuarial concept on life term insurance. The object of research is the premium on micro finance institution which is Cooperative and Public Credit Institution (LPD). The premium on the actuarial considers mortality based on age and sex, and the interest rate is set refer to the Bank of Indonesia rate of 6.5%. The result of calculation analysis shows that the higher the age of the debtor based on the actuarial calculation then the premium value will be higher, as well as the premium on LPD of Pecatu village but different with the premium on KPN of PNB. Premiums on KPN of PNB are only based on loan term so that the premium value will be the same for all ages. The actuarial calculation shows that the higher the age, chance of death are increased. Women are considered to have better insurance risk than men.

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Stochastic Interest Model Based on Compound Poisson Process and Applications in Actuarial Science

Cited by 4 publications

References 22 publications

The Bell-Touchard Counting process

The Bell-Touchard Counting process

Web renewal counting processes and their applications in insurance

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