Description: In calculations involving the distribution of total claims in a risk theory setting, several authors have found it desirable to approximate a risk-theoretic distribution by use of the incomplete gamma function. A recent paper evaluated an excess loss ratio premium by use of a gamma distribution whose first and second moments agreed with those of the risk-theoretic loss distribution. A discussion of that paper pointed out that a translated gamma distribution allowed one to make the approximate distribution agree with the risk-theoretic distribution as far as the first three moments are concerned. The method presented in this paper allows one to make as many moments of the approximate distribution as desired agree with those of the risk-theoretic loss distribution. From Transactions of Society of Actuaries 1966, Vol. 18, Pt. 1, No. 52.

Description: This presentation discusses a process for determining the minimum reinsurance retention level consistent with defined parameters. The conclusions reached were: 1. Under PDS dependence, optimal reinsurance strategy is multivariate stop loss form. 2. Explicit solutions could be derived in certain bivariate model. 3. Binding and unbinding constraints are equivalent. From Actuarial Research Clearing House, 2012, Vol. 1.

Description: This paper presents the recursive definition of the aggregate claims distribution which does not require the usual computation of the convolutions of the distribution of claim amounts. It is independent of the number of lives in the group. which makes it particularly useful for large groups. From Transactions of Society of Actuaries 1980, Vol. 32.

Description: This paper presents an introduction to collective risk theory. In collective risk theory one seeks to investigate directly the risk enterprise as a whole. Primary interest is focused not upon the gains, losses, or claims from individual policies but upon the amount of total claims or the total gain arising from all the policies in the portfolio considered. Followed by several discussion papers submitted.

Description: In the context of reinsurance, this paper addresses finding the quota share retention level and the retention limit, with a diffusion process being added to the claim process, that maximizes the adjustment coefficient in the Sparre Anderson model. From Actuarial Research Clearing House, 2006.