Description: Equity-indexed annuities [EIA's] are the fastest growing annuity products. An appealing feature of an EIA to its holder is that it contains path-dependent options which allow the policyholder to participate in favorable investment performance while maintaining a minimum guarantee on the benefit level. Studying the valuation problem of path-dependent options enables us to provide needed information to insurance companies on the costs of these options as well as investment strategy for their portfolios. The martingale approach by Gerber and Shiu [1994, 1996] enables us to solve some valuation problems in option pricing without knowing deep results in stochastic calculus such as the Reflection Principle and Girsanov Theorem. What is needed is the Laplace transform of certain distributions known by actuaries. This paper shows how to use Gerber and Shiu's approach to compute two defective density functions related to double barrier hitting probabilities of a geometric Brownian motion. The approach used here is simple and straightforward, and purely analytical. The authors then apply the formulas to value some exotic options whose payoffs are contingent on barrier hitting time.

Description: This is the abstract of a paper that derives expressions for the moments of the distribution of the option payoff in a Black Scholes economy. These results are of interest from a purely statistical viewpoint. They may also be of interest given the current importance of value at risk calculations. The paper also derives formulae for the moments of barrier options and provides numerical examples.

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: In this paper we shall present our results in terms of the estimation of human mortality rates, but the results carry over to other applications. We shall discuss a Bayesian model that encompasses both graduation [smoothing] and prediction.

Description: In estimating mortality rates from the experience of a life insurance company or employee-benefit plan, it is expedient, because of the movement into and out of the covered group on dates other than birthdays or policy anniversaries, to make some assumption about mortality over a fractional part of a year of age. This paper describes and develops the concept of 'exposure' with regard to the more commonly known methods of estimating the rate of mortality, and proposes a fourth methodology. From the Actuarial Research Clearing House 1978, Vol.2.

Description: In problem 24, Chapter 5, of Kellison's 'Fundamentals of Numerical Analysis' it is indicated how a divided difference can be expressed as a ratio of two determinants. This study note shows that this method works well also in the case where some of the arguments of collocation coincide. The rule is: If an argument occurs k times, the derivatives of the corresponding row up to order k-1 should be used in numerator and denominator.

Description: The author previously wrote about extending the general nonparallel shlft approach to duration analysis. This paper explores the immunization properties of that model. In addition, applications to asset-liability management are explored. From Actuarial Research Clearing House 1990 VOL. 2.

Description: This paper develops a theory for the valuation of some kinds of interest sensitive cash flows. A process is derived which takes as input, assumptions about the capital markets and policy holder behaviour, and produces as output interest and decrement assumptions which can be used for conventional actuarial discounting. The methodology is illustrated using some idealized, but tractable, models of conventional non-par whole life insurance. The method is also applied to a simple Universal Life plan. The paper concludes by considering some of the problems encountered when applying the ideas to more practical problems.