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The IUP Journal of Operations Management :
Some Aspects of the Barrier Probability in a Classical Risk Model
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In this paper, we have considered a classical risk model with dividend barrier, in which claim inter-occurrence times are exponentially distributed. Our aim is to obtain explicit expression for the barrier probability B(u, b), the upper barrier being assumed to be ‘b’, before ruin occurs when the claim amount distribution is either exponential or erlangian. It is to be noted that the premium loading factor is taken to be 20% in both the cases. In order to ensure fair comparison, we have chosen the exponential and erlangian parameters in such a way that their mean and hence the expected total claims are same for both the distributions over a given time interval. Ultimately, through numerical evaluation of the barrier probability for both the claim amount distributions, we investigate whether there is any significant difference between the two.

 
 

Life insurance business has always been based on actuarial principle from the beginning. The involvement of actuaries in general insurance business is of recent origin. There are various reasons for this. Life insurance policies are basically long-term contracts and by their very nature are heavily reliant on actuarial/probability calculation and there has been recognition of this fact since the beginning. In contrast, general insurance are short-term contracts and these were carried more on adhocism rather than on sound actuarial principles. The rates could always be revised at next renewal if they proved inadequate. However, the actuarial principle and methods for assessing risk under conditions of uncertainty are as much applicable to general insurance as they are to life insurance. The services of actuaries are being utilized increasingly in general insurance also in areas like pricing, claims reserving, reinsurance placement, investment and in fact in most areas of general insurance. In the days to come, more and more use of the actuarial techniques will be made in managing general insurance business and hence a proper appreciation and understanding of the same is required.

Working out ‘adequate and appropriate’ reserves is a very important aspect of the functioning of a general insurance company. It is essentially required for building up of accounts. Besides it is a regulatory requirement also. Despite the fact that reserves constitute the single largest liability on the insurer’s balance sheet, there is inadequate awareness, understanding and appreciation of the significance of these reserves and how a slight manipulation can distort the actual picture of the financial health of the company, both on short and long-term basis. In fact, the various stakeholders seldom examine the adequacy of the reserves critically.

 
 

Operations Management Journal, Some Aspects of the Barrier Probability, Classical Risk Model