Discrete-time surplus process for takaful insurance with multiple threshold levels

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Tezin Türü: Yüksek Lisans

Tezin Yürütüldüğü Kurum: Orta Doğu Teknik Üniversitesi, Uygulamalı Matematik Enstitüsü, Aktüerya Bilimleri Anabilim Dalı, Türkiye

Tezin Onay Tarihi: 2016

Öğrenci: ARHAM ACHLAK

Danışman: SEVTAP AYŞE KESTEL

Özet:

Takaful is a type of insurance system whose participants contribute a certain sum of money to a common pool in order to guarantee each other against predefined losses. Over the past few years, the global Takaful industry has maintained solid growth trajectory with significant untapped potential across several markets. For this reason, there have been numerous researches conducted on the efficiency of Takaful system, but only few of them approach its actuarial aspect. This study aims to construct a new risk model representing Takaful framework in order to develop a recursive computational procedure for some ruin-related quantities calculation associated with Takaful insurance. We consider a discrete-time Sparre Andersen model which incorporates multiple threshold levels functioning as trigger points for investment activities, loan undertakings, and dividend payments. We analyze the effectiveness of Takaful insurance by comparing its finite-time ruin probabilities and expected total discounted dividends with its conventional counterpart. Additionally, we investigate several numerical results for different Takaful business models/forms and make observations concerning the impact of some parameters used in our risk model on the ruin-related quantities.