Authors’ Reply: Credit Standing and the Fair Value of Liabilities: A Critique - Discussion by Marsha Wallace

Abstract

As investment plays an increasingly important role in the insurance business, ruin analysis in the presence of stochastic interest (or stochastic return on investments) has become a key issue in modern risk theory, and the related results should be of interest to actuaries. Although the study of insurance risk models with stochastic interest has attracted a fair amount of attention in recent years, many significant ruin problems associated with these models remain to be investigated. In this paper we consider a risk process with stochastic interest in which the basic risk process is the classical risk process and the stochastic interest process (or the stochastic return-on-investmentgenerating process) is a compound Poisson process with positive drift. Within this framework, we first derive an integro-differential equation for the Gerber-Shiu expected discounted penalty function, and then obtain an exact solution to the equation. We also obtain closed-form expressions for the expected discounted penalty function in some special cases. Finally, we examine a lower bound for the ruin probability of the risk process.     

Authors’ Reply: Economic Valuation Models for Insurers - Discussion by Jacques F. Carriere

Abstract

This article employs a longitudinal form of the Grade of Membership (GoM) model to specify and estimate a multivariate model of the trajectories of morbidity, disability, and mortality among longitudinally followed elderly respondents to the National Long-Term Care Survey (NLTCS) of 1984, 1989, 1994, and 1999. A distinct trajectory was constructed for each individual respondent to the survey. The trajectories described the progressive declines over time in physical and cognitive functioning among a nationally representative sample of the U.S. elderly population.

The model was structured to represent simultaneously the essential features of the fixed frailty model of Vaupel, Manton, and Stallard and Strehler and Mildvan’s model of linearly declining vitality. Unlike those models, however, the longitudinal GoM model was designed for easy and direct application to existing longitudinal data sets.

The measurement space in the NLTCS application included from one to four sets of repeated measures for each survey respondent on 95 independent variables characterizing the nature and intensity of limitations in activities of daily living (ADLs), instrumental activities of daily living (IADLs), physical functioning, and cognitive functioning, as well as indicators of behavioral characteristics, medical conditions, subjective health, age, race, sex, institutional status, and survival status.

The application showed that the model can be fitted to existing data and that the results were interpretable as generalizations of fixed frailty with linearly declining vitality.     

Authors’ Reply: Building Better Retirement Income Models - Discussion by Robert J. Myers; Anna Rappaport,January 1997

Abstract

In recent decades, as the use of derivatives by financial institutions has expanded, the shortcomings of historical cost accounting approaches have become increasingly apparent. Since derivatives can create large exposures to risk that go unnoticed under historical standards, the accounting industry has focused on how to change the standards so that these risks are reflected appropriately in a company’s accounting statements. New standards such as SFAS 115 and SFAS 133 have been adopted in part to achieve this goal. However, both of these standards use a piecemeal approach to risk measurement that may be adding to the problem rather than creating a solution. This paper will use a simple equity-indexed annuity to illustrate the problem with historical cost accounting and with the standards that have been adopted to correct it. The paper then argues that the only legitimate means of reflecting risk properly on a company’s accounting statements is to adopt full fair value accounting for all assets and liabilities on the company’s books.