Description: This is a 2006 draft of SOA Accreditation of Academic Actuarial Science Programs that was offered for review and comments. From Actuarial Research Clearing House, 2006.

Description: In 1995, Mexico replaced the public pay-as-you-go system by a privately managed system based on individual accounts. This paper analyzes the causes that made necessary the reform of the old Mexican pay-as-you-go pension system. A description of the modifications and current situation of the pension system also are discussed. The paper concludes that although the pension system has been modified during the last few years, there are still some weaknesses that have to be corrected to provide an appropriate retirement benefit to workers.

Description: This paper employs the theory of real option pricing to address problems in the area of operational risk management. Particularly, it develops a two-stage model to help firms determine the optimal triggers in the event of an influenza pandemic. The first stage proposes a regime-dependent epidemic model to simulate the spread of the virus, depending on whether the firm is active or inactive. The second stage views the reactivation decision as a call option and the suspension decision as a put option, and uses dynamic programming method to determine the optimal switching thresholds.

Description: For insurance companies, modeling the future values of assets and their interactions is useful for setting up asset strategies and managing reserves for liabilities. This paper evaluates the ability of Wilkie’s stochastic investment models to predict Toronto Stock Exchange [TSX] price index yield. In the Wilkie Model, correlated econometric indices are modeled through a cascade structure.

Description: A fuzzy random variable [FRV] has been conceptualized as a vague perception of a crisp but unobservable random variable [RV] and also as a random fuzzy set. Since actuaries seem receptive to these notions of FRV, and there are sources of uncertainty that RVs can not accommodate, but FRVs can, one would expect FRVs to be a component of the actuarial arsenal, but generally this is not the case. Assuming that the reason for this is that potential users are not sufficiently familiar with FRV methodology, the purpose of this article is to help alleviate this situation by presenting a FRV primer.

Description: In the classical risk theoretic model with Poisson claim arrival and exponential claims, consider the discounted value of claims nos. 3, 6, 9, and so on. [To risk theory specialists, considering every third claim in a Poisson arrival process is the same as assuming waiting times are Erlang[3] in a Sparre-Andersen model.] The distribution of the discounted value of future claims can be found. It turns out that this is the same as the distribution of the product of two independent variables, one having a gamma distribution, the other a 'complex-parameter beta product distribution'. The latter will be defined, it involves extending the usual beta distribution.

Description: There has been a growing demand for crop insurance in third world countries to combat poverty among farmers. Farmers in these countries could greatly improve crop yields if they had access to higher quality inputs, such as seeds and fertilizers. However, in order to buy these higher quality inputs the farmers need to obtain loans from microfinance institutions. These institutions are reluctant to extend loans to farmers due to the risk of loan default resulting from crop failure. With increasing abnormal weather patterns due to climate change, the concern for crop failure is on the rise and the need for such insurance is becoming more significant. Motivated by a non-governmental organization’s unsuccessful attempt to buy a crop insurance product for the farmers they serve, this paper proposes a design for rainfall indexed crop insurance for maize farmers in Kakamega, a western region of Kenya.

Description: This presentation discussed the Copula Methodology, which is the most popular methodology in multivariate modeling in finance and insurance. The definition, advantages, limitations, and uses of the Copula Methodology were presented. Some other multivariate models were discussed as well. From Actuarial Research Clearing House, 2012, Vol. 1.

Description: This presentation discusses a process for determining the minimum reinsurance retention level consistent with defined parameters. The conclusions reached were: 1. Under PDS dependence, optimal reinsurance strategy is multivariate stop loss form. 2. Explicit solutions could be derived in certain bivariate model. 3. Binding and unbinding constraints are equivalent. From Actuarial Research Clearing House, 2012, Vol. 1.

Description: This is a presentation on computing tight bounds for insurance payments with nonlinear risk. Semi-definite Programming is defined, some examples are presented, and non-linear applications are presented. From Actuarial Research Clearing House, 2012, Vol.1.