DISTRIBUSI BERSAMA DARI WAKTU KEBANGKRUTAN DAN JUMLAH KLAIM SAMPAI KEBANGKRUTAN DI DALAM MODEL RESIKO KLASIK TANPA SURPLUS AWAL; THE JOINT DISTRIBUTION OF THE TIME TO RUIN AND THE NUMBER OF THE CLAIMS UNTIL RUIN IN THE CLASSICAL RISK MODEL WITH NO INITIAL SURPLUS

Yaningrum, Paramita Tri, Adhitya Ronnie Effendie

2015 | Skripsi | FMIPA UGM

To anticipate the possibility of financial loss that may arise as a result of events that are not expected, then someone usually follow the insurance program. The policyholder is obligated to pay a sum of money to an insurance company in each period, called the insurance premiums and insurance companies provide insurance against risks that occur as agreed in the form of a sum of money called the insurance claim. If a when large capital and total premium income is smaller than a large accumulation of claims to be paid, the insurance company suffered a loss that can lead to bankruptcy. These losses are due to the amount of money that must be paid claims exceed the limits of the insurance company. But the bankruptcy process that occurs depends on the time factor, i.e when the bankruptcy, and in quantitative processes, namely the large number of claims that led to the bankruptcy case. Furthermore, we want to know the chances of a bankruptcy of an insurance company’s surplus process with exponentially distributed arrival claims. Probabilistic arguments was use to derive an expression for the joint density of the time of ruin and the number of claims until ruin in the classical risk model. From this, a general expression for the probability function of the number of claims until ruin. The moments of the number of claims until ruin was considered and illustrated the results in the case of exponentially distributed individual claims. A very strong correlation was found between the number of claims until ruin and the time of ruin in the classical risk model with no initial surplus.

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