Description: This paper develops credibility using a longitudinal data framework. In a longitudinal data framework, one might encounter data from a cross-section of risk classes towns with a history of insurance claims available for each risk class. For the marginal claims distributions, we use generalized linear models, an extension of linear regression that also encompasses Weibull and Gamma regressions. Copulas are used to model the dependencies over time specifically, this paper is the first to propose using a t-copula in the context of generalized linear models. The t-copula is the copula associated with the multivariate t-distribution like univariate t-distributions, it seems especially suitable for empirical work. Moreover, we show that the t-copula gives rise to easily computable predictive distributions that we use to generate credibility predictors. Like Bayesian methods, our copula credibility prediction methods allow us to provide an entire distribution of predicted claims, not just a point prediction.

Description: A framework to measure and evaluate the risk-adjusted investment performance given the characteristics of the insurance liability.

Description: This paper examines claim transaction data as experienced in the Canadian pet insurance industry. The current practice is to use an exposure unit approach to estimate the pure premium cost. This approach is applied in this paper in order to reveal certain cost patterns in accident, illness and death benefit costs.

Description: This session at the 1998 Valuation Actuary Symposium gives an overview of risk management. Two example company programs are described. The use of value at risk as a measure is discussed.

Description: Studies default risk through the two-sided exit problem of a time-homogeneous di§usion process with tax payments of loss-carry-forward type and obtains explicit formulas for the exit probabilities. If the lower boundary is understood as the default threshold, then the nondefault probability is solved as a special case. A sufficient and necessary condition for the tax identity is discovered.

Description: Part one of a two-part article, to be contined in Feb 2014. Provides useful rules of thumb for breaking out investment return into components of periodic arithmetic return, geometric return, the volatility of returns and the correlation of returns by asset class. Develops and relates these axiomatic concepts into rules of thumb for estimating quantiles of a range of stochastic returns.

Description: In this essay, we focus on the “Prospective Solvency Assessment” aspect of the NAIC’s ORSA. This places a spotlight on an insurer’s strategic decision making from a risk and capital management perspective. It requires those in senior management to describe actions they would take to address possible adverse changes in their risk and solvency position, i.e., what they would do to reduce risk, increase capital, and/or adjust the business strategy. We contend that by applying a slightly broader scope than the specific requirements of the NAIC’s ORSA, insurers can develop this into a valuable process to support risk-based decision making. In this essay, we initially consider how to determine which metrics to include in such a process and then discuss some important business requirements and practical challenges for implementing a calculation approach to support it. Part of the essay collection "Risk Metrics for Decision Making and ORSA"

Description: This paper investigates the optimal multi-period proportional reinsurance strategy that minimizes the ruin probability of an insurer. Some conditions under which it is optimal to have no reinsurance are derived. Based on these results, a new concept, capital threshold of proportional reinsurance, is introduced. In the case of two periods, a lower bound of the capital threshold of proportional reinsurance is provided. Some economic implications and properties of this new concept are also discussed.

Description: Discusses bond-default history in the United States, implications for insurance-company asset determination, regulatory concerns about recent investing by insurance companies in low-grade bonds, valuation-actuary needs to consider in these cases, and another suggested method for modeling the C-1 Risk in the context of the valuation actuary's cash flow review. From the 1987 Record of Society of Actuaries, Vol. 13, No. 3.

Description: Statistical properties of interest, annuity and insurance functions are examined when mortality and interest are treated as having a random component. Several special models of interest rate fluctuation are examined in detail. It is hoped that such theory will be useful in developing fluctuation reserves and premium margins. Presented at the 13th Annual Actuarial Research Conference, Ball State University, August 31st. September lst, 2nd. 1978.