Question

Claim data show that the claim in each period has mean 0.8 and variance 0.4. Assuming the claim process follows a Poisson process and the premium has a loading of 10%, determine the approximate bound of the probability of ultimate ruin if the initial surplus is 4 . If it is desired to reduce this bound by 10%, what will be the revised premium loading without increasing the initial surplus? If the premium remains unchanged, what is the required initial surplus to achieve the desired probability bound of ultimate ruin?

Answer 1

The student's question requires an understanding of risk theory and actuarial science, including the use of the Lundberg inequality and calculations related to insurance premium adjustments and initial surplus requirements to influence the probability of ultimate ruin.

Step-by-step explanation:

The question is related to the concept of risk theory and actuarial science, particularly focusing on determining the probability of ultimate ruin under a Poisson claim process and adjusting premium loadings to affect this probability. An actuarially fair premium is a premium that is set such that the expected value of the insurance payments equals the expected value of the claims.

In the given scenario, an initial surplus of 4 and a premium with a 10% loading have been considered with claim data showing a mean of 0.8 and variance of 0.4. To calculate the approximate bound of the probability of ultimate ruin under these conditions, the Lundberg inequality for the Poisson risk process can be applied. To reduce the bound by 10%, a revised premium loading needs to be determined without increasing the initial surplus. Alternatively, if the premium remains unchanged, a calculation is required to identify the necessary initial surplus to achieve the desired reduction in the probability bound of ultimate ruin.