The Measure Of The Severity Of Ruin In Risk Model With Debit Interest

The main aim of this paper is to study the maximum of the severity of ruin in risk model with debit interest.The risk model with debit interest which is based on the classical model, firstly proposed by Gerber(1971), is a more practical risk model. Assume that the surplus of an insurer follows a compound poisson surplus process perturbed by diffusion. When the surplus is below zero or the insurer is on debit, the insurer could borrow money at a debit interest rate to continue her business. Meanwhile the insurer will repay debt from her premium income. We assume that an insurer is allowed to continue her business with debt as long as her is at a reasonable level. However, when the debt or negative surplus is below some certain critical level, the insurer is no longer allowed to run his business. Absolute ruin occurs at this situation. In this risk model, absolute ruin may be caused by a claim or by oscillation. The absolute ruin probability can be decomposed to the sum of two ruin probabilities, one is the probability that absolute ruin is caused by a claim and other is the probability that absolute ruin is caused by oscillation. In this paper, the maximum of the severity of ruin in the classical model with debit interest is derived by means of the approach used in classical model by Picard (1994). This paper includes four chapters. The first chapter is introduction. In the second chapter, the risk model with debit interest and some useful results are introduced. In the third chapter, through analysis of the risk model with debit interest, using the technique of moving figure. Then the maximum of the severity of ruin of the risk model with debit interest are derived. The last chapter gives a conclusion.