“Relative Importance of Risk Sources in Insurance Systems”, Edward W. Frees,April 1998

Abstract

This paper considers a Sparre Andersen collective risk model in which the distribution of the interclaim time is that of a sum of n independent exponential random variables; thus, the Erlang(n) model is a special case. The analysis is focused on the function φ(u), the expected discounted penalty at ruin, with u being the initial surplus. The penalty may depend on the deficit at ruin and possibly also on the surplus immediately before ruin. It is shown that the function φ(u) satisfies a certain integro-differential equation and that this equation can be solved in terms of Laplace transforms, extending a result found in Lin (2003). As a consequence, a closed-form expression is obtained for the discounted joint probability density of the deficit at ruin and the surplus just before ruin, if the initial surplus is zero. For this formula and other results, the roots of Lundberg’s fundamental equation in the right half of the complex plane play a central role. Also, it is shown that φ(u) satisfies Li’s (2003) renewal equation. Under the assumption that the penalty depends only on the deficit at ruin and that the individual claim amount density is a combination of exponential densities, a closed-form expression for φ(u) is derived. In this context, known results of the Cauchy matrix are useful. Surprisingly, certain results are best expressed in terms of divided differences, a topic deleted from the actuarial examinations at the end of last century.     

“Economic Capital Allocation Derived from Risk Measures”, Eddy Van den Borre,January 2003

Abstract

The sustained reduction in mortality rates and its systematic underestimation has been attracting the significant interest of researchers in recent times because of its potential impact on population size and structure, social security systems, and (from an actuarial perspective) the life insurance and pensions industry worldwide. Despite the number of papers published in recent years, a comprehensive review has not yet been developed.

This paper attempts to be the starting point for that review, highlighting the importance of recently published research—most of the references cited span the last 10 years—and covering the main methodologies that have been applied to the projection of mortality rates in the United Kingdom and the United States. A comparative review of techniques used in official population projections, actuarial applications, and the most influential scientific approaches is provided. In the course of the review an attempt is made to identify common themes and similarities in methods and results.

In both official projections and actuarial applications there is some evidence of systematic overestimation of mortality rates. Models developed by academic researchers seem to reveal a trade-off between the plausibility of the projected age pattern and the ease of measuring the uncertainty involved. The Lee-Carter model is one approach that appears to solve this apparent dilemma.

There is a broad consensus across the resulting projections: (1) an approximately log-linear relationship between mortality rates and time, (2) decreasing improvements according to age, and (3) an increasing trend in the relative rate of mortality change over age. In addition, evidence suggests that excessive reliance on expert opinion—present to some extent in all methods—has led to systematic underestimation of mortality improvements.     

Risk,Capital, and Operating Efficiency: Evidence from Taiwan’s Life Insurance Market

ABSTRACT

In this article, we investigate the relationships among risk, capital, and operating efficiency for Taiwanese life insurance companies from 2004 to 2009 by using the two-stage least-square approach. We find a positive relation between inefficiency and product risk. At the same time, efficient insurers are seen as taking higher asset risk than inefficient insurers. A contrasting finding also shows that the relationship between capital and product risk is positive, while the relationship between capital and asset risk is negative. Moreover, we present a negative relationship between inefficiency and capital level, indicating that well-capitalized insurers operate more efficiently than poorly capitalized insurers.     

“Modeling the Impact of Genetics on Insurance”, Angus S. Macdonald,January, 1999

Abstract

Current formulas in credibility theory often estimate expected claims as a function of the sample mean of the experience claims of a policyholder. An actuary may wish to estimate future claims as a function of some statistic other than the sample arithmetic mean of claims, such as the sample geometric mean. This can be suggested to the actuary through the exercise of regressing claims on the geometric mean of prior claims. It can also be suggested through a particular probabilistic model of claims, such as a model that assumes a lognormal conditional distribution. In the first case, the actuary may lean towards using a linear function of the geometric mean, depending on the results of the data analysis. On the other hand, through a probabilistic model, the actuary may want to use the most accurate estimator of future claims, as measured by squared-error loss. However, this estimator might not be linear.

In this paper, I provide a method for balancing the conflicting goals of linearity and accuracy. The credibility estimator proposed minimizes the expectation of a linear combination of a squared-error term and a second-derivative term. The squared-error term measures the accuracy of the estimator, while the second-derivative term constrains the estimator to be close to linear. I consider only those families of distributions with a one-dimensional sufficient statistic and estimators that are functions of that sufficient statistic or of the sample mean. Claim estimators are evaluated by comparing their conditional mean squared errors. In general, functions of the sufficient statistics prove to be better credibility estimators than functions of the sample mean.     

An Approach to Fair Valuation of Insurance Liabilities Using the Firm’s Cost of Capital

Abstract

There are two competing and seemingly different methodologies for calculating fair values—the direct and indirect methods. The direct approach has the advantage of providing a more reliable assessment of the risk of financial leverage. The indirect method can be structured to adjust for financial leverage, however, the methodology becomes excessively complex. The advantage of the indirect method is that it can be more easily related to exit prices. Intuitively, an exit price should reflect both the creditworthiness of the firm and the cost of capital of the firm. How are these two concepts related? This paper attempts to advance the fair valuation methodology by addressing these questions and presenting a methodology for deriving the firm or own credit risk assumption (to be used with the direct method) that is consistent with the cost of capital assumption used with the indirect method.     

Insurance and Endogenous Bankruptcy Risk: When is it Rational to Choose Gambling,Insurance, and Potential Bankruptcy?

We examine the coexistence of insurance and gambling in the context of limited liability. We develop a model where actuarially fair insurance is available to a risk-averse decision maker for a liability risk with non-bankrupting severity. The remaining wealth may be invested in a zero expected value risky project (i.e., gambled). The risk of bankruptcy is endogenous since either fully insuring or forgoing the project will guarantee solvency. We show that, for a range of parameters, it is optimal to both insure and gamble. The amounts insured and invested are chosen to create the potential for bankruptcy. Our results are robust to the cases where the risky project can cause bankruptcy without a liability loss and where the risky project’s expected return is nonzero.     

“Bounds for Ruin Probabilities in the Presence of Large Claims and their Comparison”, Vladimir Kalashnikov,April, 1999

Abstract

Performance measurement systems and report cards which attempt to measure and report the quality of care provided by managed health-care organizations, have become mainstream in health insurance markets as managed care penetration continues to increase. However, little is known about the impact formal plan evaluations have on the contracting and enrollment decisions made by health insurance purchasers and consumers. Information regarding the link between performance evaluations and enrollment is crucial for those charged with projecting future enrollments in and risk profiles of managed care organizations. This paper describes the performance measurement systems currently being used to evaluate managed care plans and reviews the empirical literature for evidence regarding the impact of measures on plan enrollments.     

“The Future of Risk Classification in the Age of Predictive DNA-Based Testing”, Donald C. Chambers,January 1999

Abstract

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. To address this issue, we study a Bayesian log-normal model in the prediction of outstanding claims for dependent lines of business. In addition to the pairwise correlation, our method allows for an explicit examination of the correlation due to common calendar year effects. Further, different specifications of the calendar year trend are considered to reflect valuation actuaries’ prior knowledge of claim development. In a case study, we analyze an insurance portfolio of personal and commercial auto lines from a major U.S. property-casualty insurer. It is shown that the incorporation of calendar year effects improves model fit significantly, though it contributes substantively to the predictive variability. The availability of the realizations of predicted claims permits us to perform a retrospective test, which suggests that extra prediction uncertainty is indispensable in modern risk management practices.     

“The Current State of Genetic Testing: An Insurance Industry Perspective on the Rush to Legislate”, Charles S. Jones,Jr., January, 1999

Abstract

We propose a new type of retirement plan, aimed at achieving a compromise between stability in cost for the plan sponsor and guaranteed accumulation for the participants. The behavior of the plan is compared with that of a money purchase plan for both deterministic and stochastic investment scenarios. The proposed plan is shown to provide more stable and predictable benefits than a money purchase plan. Obstacles to the establishment of such a plan, from the perspective of U.S. pensions legislation, are considered.     

Discussion of “Evaluating Non-GAAP Performance Measures in the REIT Industry”

Review of Accounting Studies -