Facultative Reinsurance Limit Using Tail Value at Risk (TVaR) of Bank Loans with Mixture Distribution Utriweni Mukhaiyar (a*), David Eurico (b), Bagas Caesar Suherlan (b), Afifatul Ayu Astiani (b), I Kadek Darma Arnawa (b)
a) Statistics Research Division, Faculty of Mathematics and Natural Science, Institut Teknologi Bandung, Jl. Ganesha No. 10 Bandung 40132, Indonesia
*utriweni.mukhaiyar[at]itb.ac.id
b) Master Program in Actuarial Science, Faculty of Mathematics and Natural Science, Institut Teknologi Bandung, Jl. Ganesha No. 10 Bandung 40132, Indonesia
Abstract
In general, Bank does lend loans to the public. Recent regulation suggests that a certain Bank should sign a facultative reinsurance contract as a protection for default risk of 15% of loans with the highest principal. This research is aimed to find the limit of the largest 15% of loans using Tail Value at Risk (TVaR) method since it seeks the expectation of the loan principal that will be protected under a facultative reinsurance contract. The 5,000 samples^ principal of the certain Bank loans be investigated. The behavior of these loans can be described by Mixture Gamma distribution with three components whose proportions and parameters are different. Those are 19% of Gamma with \(\alpha \) = 2.45, \(\beta\) = 0.04, 34.5% of Gamma with \(\alpha \) = 8.29, \(\beta\) = 0.07, and 46.5% of Gamma with \(\alpha \) = 30, \(\beta\) = 0.13. Furthermore, the limit of the facultative reinsurance contract obtained through TVaR is 274.9 million rupiah. The new loans with principal above the number before will automatically be protected under facultative reinsurance contract.
Keywords: Bank- Facultative Reinsurance- Mixture Distribution- Risk- Tail Value at Risk
