2Hacettepe University, Department of Actuarial Science, ANKARA
This paper introduces a hazard rate function for the time of ruin to calculate the conditional probability of ruin for very small time intervals. We call this function as the force of ruin (FoR). We obtain the expected time of ruin and conditional expected time of ruin from the exact finite time ruin probability with exponential claim amounts. Then, we introduce the FoR which gives the conditional probability of ruin and the condition is that ruin has not occurred at time t. We analyse the behaviour of the FoR function for different initial surpluses over a specific time interval. We also obtain FoR under the excess of loss reinsurance arrangement and examine the effect of reinsurance on the FoR.