This paper proposes a model for measuring risks for derivatives that is easy to implement and satisfies a set of four coherent properties introduced in Artzner et al. 1999. We construct our model within the context of Gerber-Shiu's option-pricing framework. A new concept, namely Bayesian Esscher scenarios, which extends the concept of generalized scenarios, is introduced via a random Esscher transform. Our risk measure involves the use of the risk-neutral Baysian Esscher scenario for pricing and a family of real-world Bayesian Esscher scenarios for risk measurement. Closed-form expressions for our risk measure can be obtained in some special cases. From NAAJ, July 2001, Volume 5, Number 3.

In this session we will revisit some of the actuarial applications of Bayes’ theorem that Sharon McGrayne covered in Part I. The aim is to present more technical details as well as to highlight some of the shortcomings of work that was completed almost a century ago, well before high-speed computing tools had appeared on everyone’s desks. The session will also discuss some of the more modern actuarial applications of Bayes’ theorem. Other applications to pro football and the U.S. Olympic Team will be discussed.

The speaker, journalist/writer Sharon McGrayne, is the author of the book, The Theory That Would Not Die. She will summarize sections of her book that describe groundbreaking work of actuaries who were among the earliest practitioners to apply Bayes’ theorem to important real-life problems. These actuaries include Albert Whitney, Arthur Bailey and L.H. Longley-Cook. Actuaries often refer to this area of actuarial science as “credibility.” There will be no sophisticated mathematics discussed in this session.

This paper uses a Bayesian framework to compare discrete distributions for claim counts. It includes examples on 8 data sets.

This is a discussion of a previously published paper, "A Bayesian Generalized Linear Model for the Bornhuetter-Ferguson Method of Claims Reserving" part one.

This is a discussion of a previously published paper, "A Bayesian Generalized Linear Model for the Bornhuetter-Ferguson Method of Claims Reserving" part two.

This is a discussion of a previously published paper, "A Framework For Long-Term Actuarial Projections of Health Care Costs: The Importance of Population Aging and Other Factors."

This paper is concerned with the situation that occurs in claims reserving when there are negative values in the development triangle of incremental claim amounts. It also presents a Bayesian model to consider negative incremental values, based on a three-parameter lognormal distribution. The model presented here allows the actuary to provide point estimates and measures of dispersion, as well as the complete distribution for outstanding claims from which the reserves can be derived. It is concluded that the method has a clear advantage over other existing models. A Markov chain Monte Carlo simulation is applied.

The correlation among multiple lines of business plays an important role in quantifying the uncertainty of loss reserves for insurance portfolios. To accommodate correlation, most multivariate loss-reserving methods focus on the pairwise association between corresponding cells in multiple run-off triangles. However, such practice usually relies on the independence assumption across accident years and ignores the calendar year effects that could affect all open claims simultaneously and induce dependencies among loss triangles.

The NAAJ is honoring the Society of Actuaries on its golden anniversary in 1999 by publishing a series of articles on the contributions of actuaries to the development of ideas. In this issue, the second of the series, we explore the development of the credibility idea and the relationships of this development to deep issues in the methodology of science. We begin with a short essay by James C. Hickman and continue with comments by three actuaries who were deeply involved with the development of credibility: Robert A. Bailey, Hans Buhlmann, and Chrles C. Hewitt. From NAAJ, April 1999, Volume 3, Number 2.