Description: This paper is to some extent a sequel to my previous paper A Bond Manager's Method for ALM published in Actuarial Research Clearing House Volume 1993.3. It borrows from that paper the concept of benchmark weights for measuring the sensitivity of the present value of a set of cash flows to changes in interest rates. However, a completely different approach to calculating benchmark weights is presented.

Description: In this expository paper several comments are made with respect to the statistical independence of the curtate future lifetime and the fractional part of the future lifetime, both of a general status. In particular, the conditions for independence need to be stated carefully. The last-survivor status is cited as an example. More general assumptions than the uniform distribution of deaths assumption are then considered, together with applications to insurances, annuities, and reserves. Similar results to those under the uniform distribution of deaths assumption are obtained. Brief comments are made with respect to contingent probabilities in multiple lives and multiple decrement theory.

Description: It is obvious that the introduction of a deductible has two major effects. The amount paid for every claim will drop, resulting in a lower claim burden for the insurance company. There will also be a drop in claim frequency, leading to a decrease in claim handling expenses. However, it is by no means obvious how the average claim size changes with the introduction of a deductible. In this paper, we will study this question. First, we derive some theoretical results then apply them to concrete distributions.

Description: This is a study on the Nesbitt formula and the variants to this formula.

Description: We consider a class of compound renewal risk process with claim waiting times have a discrete Km distribution. The classical compound binomial risk model is a special case when m = 1. Both recursive and explicit formulas are derived for the expected discounted penalty function due at ruin, for the surplus before ruin and the deficit at ruin. Many ruin related quantities can be analyzed through the penalty function, e.g., ruin probability, the p.g.f. of the time of ruin, joint and marginal distributions of the surplus before ruin and the deficit at ruin, claim causing ruin, as well as their moments. Detailed discussions are given in two special cases: claim sizes are rationally distributed, or the claim sizes distribution have a finite support.

Description: This is a simplified approach to calculating the variance of the whole life random variable in certain, very common circumstances.

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: The costly, time-consuming and complicated process of enterprise risk management (ERM) can be improved in many companies and made less tedious for managers by using reasonable data and templates obtained from peer group entities. The models used to calculate economic capital (EC) often underestimate its value because they do not consider decision-maker perception about risk. We assume here that managers, as the decision-makers, have appropriate business understanding and they can provide substantial information about risk characteristics regarding all business processes. Therefore we are focused, in this paper, on collecting data from managers across the different businesses to derive the appropriate knowledge about risky events, the importance of particular types of risk, the relationship between the risk outcomes and the level of risk control in a particular industry. We conclude that the collected data has a high potential for use as a benc hmarking reference and analysis for improving ERM models for individual businesses.

Description: In 1993, the Chicago Board of Trade introduced a futures contract on a financial index that reflects the insurance claims emerging from catastrophes in a portfolio of policies. This article presents a valuation formula for the contract, under the assumption that catastrophes emerge as a Poisson process over time and that the claims from each catastrophe emerge as a Compound Poisson process. The formula is developed by taking conditional expectations with respect to a history of information that includes knowledge about the time of the catastrophes.

Description: This paper deals with how the credibility levels change based on this lack knowledge. Group insuraace models are used, bill some of tile techniques could apply to any insurance risk.