Ruin Probabilities Simulation of Insurance Company Based on Premium and Claim Size Data Utriweni Mukhaiyar (a*), Febrina Puspa S. (b), Yovia Galuh S. (b), Elonasari (b), Rusniwati S. Imran (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
Insurance company releases insurance products at the most competitive prices based on the demographics of the potential participants. The greater the number of participants or premiums earned at any given time, the greater the company^s source of income that can be used to cover the amount of claims that may occur. On the other hand, for participants who have paid a number of premiums, guarantees for risks that may arise will be borne by the company after the claim is submitted. In order for the insurance company^s financial reserves to continue to pay all incoming claims, the company must be able to predict the worst possible event so that it can be avoided, that is the bankruptcy. Ruin probability is estimated by a simulation using the general model of the company^s financial reserves. The simulation is based on gamma distributed insurance claim sizes data. Premiums are divided into 10 levels, with the difference of 5 USD in each level, start from 40 USD at first level till 85 USD at the 10th level. The simulation shows that the insurance company^s reserves at USD7 million, USD1 million, USD200 thousand, and USD5 thousand, all at premiums USD40 (first level), will have the biggest number of ruin probability but the longest day of first day of bankruptcy. They are, sequentially, 0.01 on the 356th day, ruin probability at 0.67 on the 122nd day, probability 0.93 on the 34th day, and 0.97 on the 14th day. The bigger amount of premiums, the smaller its probability of ruin. At insurance company^s reserve USD 5 thousand, the number of ruin probabilities are greater than 0, almost at all premiums level.
