| Summary: | 碩士 === 國立臺北大學 === 統計學系 === 92 === To calculate ruin probabilities, we need a coefficient called “adjustment coefficient”. But it doesn’t always exist. So many scholars offer methods to calculate ruin probabilities when adjustment coefficient does not exist. J.Cai&J.Garrido (1999) “Two-sided bounds for ruin probabilities,” Dickson (1994) “An Upper Bound for the Probability of Ultimate Ruin” and Steve Drekic and Gordon E.Willmot (2003) “On The Density and Moments of the Time of Ruin with Exponential Claims.” In this paper, we use the compound Poisson risk model and suppose the claims size is a mixed exponential distribution. Because the traditional method to calculate ruin probabilities need the adjustment coefficient and the method is complex. So we are also interesting in these method that can instead of the traditional method even when the adjustment coefficient exist. Then in several cases, we compare these methods and show the result. Our goal is to find which method is powerful and useful and which method is better for different conditions. After comparisons, we find two important points. First even if the adjustment coefficient exists, J.Cai&J.Garrido’s method is good enough to instead of traditional method. Second Steve Drekic and Gordon E.Willmot’s method is calculating the ruin probabilities of a period is better than other methods to calculate the ultimate ruin probabilities.
|
|---|
