DISTRIBUSI GABUNGAN ANTARA WAKTU HINGGA TERJADINYA KEBANGKRUTAN DAN JUMLAH KLAIM HINGGA TERJADINYA KEBANGKRUTAN DALAM MODEL RESIKO KLASIK UNTUK KASUS SURPLUS AWAL LEBIH BESAR DARI NOL; ( THE JOINT DISTRIBUTION OF THE TIME TO RUIN AND THE NUMBER OF CLAIMS UNTIL RUIN IN THE CLASSICAL RISK MODEL FOR CASE INITIAL SURPLUS MORE THAN ZERO )

Haris, Yusvaldo Baresh, Adhitya Ronnie Effendie

2015 | Skripsi | FMIPA

To reduce the impact arising from a risky event that could cause a substantial financial loss, then someone usually using insurance services. The insurance company will guarantee insurance users to avoid the risk of events that can lead to insurance users having a substantial financial losses. While users insurers have an obligation to pay a certain fee to the insurance company, the costs paid to the insurance company known as the premium. If the amount of premiums paid to the insurance company still not be sufficient for compensation to be provided to users of insurance, it can lead to bankruptcy 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 companys surplus process with exponentially distributed arrival claims. Using probabilistic arguments 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 we obtain a general expression for the probability function of the number of claims until ruin. Consider the moments of the number of claims until ruin and illustrate our 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 initial surplus more than zero.

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