Ambang Batas Reasuransi Non-Proporsional Menggunakan Tail Value-At-Risk (TVaR) dari Distribusi Peluang Campuran

Abstract

One of the tasks of banking institutions is to channel funds to the public through loan products. Banking institutions transfer the risk of non-performing loans to insurance companies and then partially reinsured to reinsurers. The purpose of this study is to determine the non-proportional reinsurance threshold based on the risk of loss of the 20% largest loan principal, using the Tail Value-at-Risk (TVaR) method. The threshold value will be estimated using a sample of 5,000 loans principal. The loan characteristics can be described by a Mixture Gamma Distribution consisting of components with different weights and parameters. The weights and parameters are 19% from the Gamma distribution with parameters α = 2.45 and β = 0.04, 34.5% from Gamma with parameters α = 8.29 and β = 0.07, and 46.5% from Gamma with parameters α = 30 and β = 0.13. Analysis using TVaR produces a threshold value of 274.9 million rupiah. In real cases, if the claim value exceeds 274.9 million rupiah. The insurance company will bear a value of 274.9 million rupiah and the reinsurer will bear the difference in the size of the claim against the threshold limit.