Description: This is a concluding and encompassing part of our research on the project entitled \Weighted Premium Calculation Principles and Risk Capital Allocations, which has been supported by the Actuarial Education and Research Fund AERF and the Society of Actuaries Committee on Knowledge Extension Research CKER. We explore the concept of weighted distributions and their role in various phenomena occurring in insurance and finance. In particular, we relate weighted distributions to actuarial and economic premium calculation principles, and also to the capital asset pricing model CAPM. Imitating the latter, we propose a weighted insurance pricing model WIPM. Although general in formulation, we show that the WIPM can successfully be evaluated in a variety of situations, which we illustrate with a number of examples.

Description: In addition to death and maturity guarantees on the mutual funds they sell, some insurance companies make it possible for the investor to extend the guarantees for a fixed number of years. In this paper, we consider the case when that option is of the European type that is, the investor, at maturity, can either close out the contract or extend it for the stated, fixed term. When extended, the guarantee is on the value of the fund at the original maturity date. The fund is assumed to be fully invested in common stock.

Description: An insurance company starts with an initial surplus, collects premium, pays claims to policyholders and pays dividends to stockholders. What remains is the following year’s surplus. The process continues. This paper describes how to calculate the distribution of surplus for any given year. With these distributions, one can make the calculations of premiums and dividends.

Description: In this paper we discuss some properties of the nth stop-loss order and their application in risk premium principles. We give a necessary condition and a sufficient condition for nth stop-loss orders. They are convenient tools to construct risk pairs with nth stop-loss orders. We show that exponential premium principles can diferentiate between losses more finely than the net premium principles under some conditions.

Description: This is a summary of the presentation given during the ARC Conference. Its purpose was to give a brief introduction to subexponential behavior and to show that the family of subexponential distributions provides ideal characteristics to model insurance risks. Although the literature related to this topic accumulated quickly during the last years, a textbook explaining the applications of extreme value theory with intuition as well as insight was still to be written. Embrechts et al, {I 997} satisfies this need and most of the results presented here can be found in this new classic in the actuarial literature.

Description: This paper thoroughly describes risk premium calculation based on an insurance portfolio consisting of policies risks insured over a finite time interval.

Description: This paper examines claim transaction data as experienced in the Canadian pet insurance industry. The current practice is to use an exposure unit approach to estimate the pure premium cost. This approach is applied in this paper in order to reveal certain cost patterns in accident, illness and death benefit costs.

Description: In a series papers by Willmot and Lin, both exponential and non-exponential bounds for the tail probability of various compound distributions have been derived. In Wilmot, it was suggested that non-exponential bounds for the ruin probability were difficult to obtain using martingale arguments. In this note, we show how to use martingale inequalities to obtain some upper bounds for the ruin probability.

Description: The paper o ers a simple framework for ranking the common reinsurance struc- tures in practice with the theory of stochastic orders. The basic idea is to slice the space of reinsurance structures into groups by expected loss cost to facilitate the comparisons within the group and between groups. Given the standard risk aversion assumption in economics, a spectrum of reinsurance structures with the same expected loss cost can be compared analytically with one another and sequenced based on their risk coverages under the convex order. The paper then expands the dimension of the comparison to groups of reinsurance structures with di erent expected loss costs, which can be ranked under the increasing convex order and the usual stochastic order. As such, the paper maps out the ordering for the entire space of reinsurance structures and presents it in a ma- trix format for quick reference. The implication

Description: In Volume LXXV of the Proceedings there appeared a paper entitled Risk Loads for Insurers by Feldblum. Confidence intervals for the betas in TABLE 4 [Profit Margins and Their Standard Deviations by Line of Business] of this paper can be generated using the assumption of underlying normal distributions. However, bootstrapping operational or not for interval estimates does not require the normality assumption. The method of operational bootstrapping does not use random numbers. The method for the 4-dimensional case, used to generate the interval estimates in the current paper, is a natural generalization of the bivariate case. I use operational bootstrapping to generate interval estimates for Betas shown in the TABLE 5.