Absolute Ruin In The Compound Poisson Risk Model With Threshold Dividend Strategy

Absolute ruin means that when the surplus process is below zero,the insurer could borrow money at a debit interest rate to continue her business. Mean while,the insurer will repay the debts from her premium income. We assume that an insurer is allowed to continue her business with debts until her debts or negative surplus is below some certain level, and in the latter case, the insurer is no longer allowed to run her business, absolute ruin occurs at this situation. By this means, in the present paper, we investigate the absolute ruin problem in the compound Poisson risk model with threshold dividend strategy.We first derive integro-differential equations for the expected discounted value of all dividends until absolute ruin and expected discounted penalty function. In the case of exponential claim amounts, we obtain explicit expressions for m(u; b)and absolute ruin probability (?)(u;b).