Description: The dependent relationship between two lives is readily analyzed within the context of probability theory. This paper presents useful relationships between certain actuarial and probability functions and then explores measures of dependence. From Transactions of Society of Actuaries 1986, Vol. 38.

Description: The American Academy of Actuaries and the Society of Actuaries have joined resources to maintain this Economic Scenario Generators Excel Workbook tool for use in regulatory reserve and capital calculations. Please see the SOA website research pages for further information on this tool and how to use it.

Description: This paper studies the joint distribution of the time of ruin, the surplus immediately before ruin, and the deficit at ruin. The classical model is generalized by discounting with respect to the time of ruin. The authors show how to calculate an expected discounted penalty, which is due at ruin, and may depend on the deficit at ruin and the surplus immediately before ruin.

Description: Most computations that are done within actuarial science entail using discrete death rates associated with incremental ages. It's not that continuous death rates cannot be used, it's just that discrete values tend to be more convenient to work with. Of the various continuous probability distributions, the one most closely associated with actuarial science may be the Gompertz distribution. This paper takes a closer look at the Gompertz, starting with the motivation behind Benjamin Gompertz proposing this particular distribution. Then the paper develops procedures to estimate the parameters for this distribution, and it ends with a brief example of the procedures presented in the paper.

Description: Many insurers preparing market consistent financial statements encounter the issue of developing volatility assumptions for equity options and guarantees that are longer than any observable market data. This presentation develops a generalization of the classical Black Scholes option pricing model that is consistent with the European CRO Forum's framework for valuing non-hedgeable risk. The presentation argues that, with reasonable parameter choices, the model fits observed volatility surfaces well enough that it can be used to estimate implied volatilities where no market data exists.

Description: The theme of this paper relates to solving portfolio selection problems using linear programming. The authors extend the linear optimization framework for Conditional Value-at-Risk-based portfolio selection problems to optimization over a more general class of risk measure known as the class of Coherent Distortion Risk Measure. From Actuarial Research Clearing House, 2012 Vol. 1.

Description: This article poses the question, why doesn't the teaching of life contingencies start with the premise that the rate of investment income is a random process in a similar manner to the random nature of the time until death? The article suggests some methods for doing so.

Description: The theme of this presentation relates to solving portfolio selection problems using linear and fractional programming. Two key contributions: 1. Generalization of the CVaR linear optimization framework. 2. Equivalences among four formulations of Coherent Distortion Risk Mearures optimization problems. From Actuarial Research Clearing House, 2012, Vol. 1.

Description: The purpose of this paper is to explain several actuarial-demographic-statistical techniques and show their application in medical investigations. Actuarial Research Clearing House 1979, VOL. 1

Description: Article describing content and key takeaways from experience completing the SOA PA Certificate