On Some Measures Of The Severity Of Ruin In The Compound Poisson Model With Debit Interest Rate

In this paper, we mainly studied some measures of the severity of ruin in the compound poisson model with debit interest rate.The compound poisson model with debit interest rate, firstly proposed by Gerber(1971). It is further expansion of the compound poisson model. When surplus is negative, the company debit from the bank in order to continue to manage, and of course they have to pay interest. Enlightened by Picard(1994), we get some measures of the severity. First we introduce a pair function (f,g), then we get the expectation and the variance of the linear sum, the expectation of the duration and the cost from ruin to recovery or absolute ruin followed exponential claim through constructing martingale. Then, we obtained the probability function, the expectation, the variance, and the moment generating function of recovery number.This paper includes four chapters. The first chapter is introduction. In the second chapter, the compound piosson model with debit interest rate and some useful results are introduced. The martingale theory is embodied in the third chapter-the main body of this paper, and then we calculate several measures of the company's severity of ruin. The last chapter gives a conclusion.