Description: This paper develops an option pricing model that takes cost of capital concepts as its foundation rather than dynamic replication. The resulting model, called the 'C' measure in this paper, is related to the family of Affine Jump Diffusion models that are well known in the finance literature, so it is fairly easy to understand and implement. We argue that this is a reasonable model to use for estimating equity implied volatilities that are beyond the five- to 10-year horizon that can typically be observed in today‘s capital markets. The paper concludes with a short discussion of how to grade from observable market data to the 'C' measure.

Description: In this paper,we present a method which first converges a two dimensional data to a univariate one and then uses the interval censoring technique to estimate the probability of failure of a Joint-life status from a heavily censored data. Our study shows that the life annuities of joint-life status calculated assuming independence overestimates the ones evaluated from an actual sample of population.

Description: By the use of resampling and extreme value statistics we will develop a method to reduce the time and costs of testing insurance company insolvency. Most ruin models require assumptions about the surplus distribution and/or assumptions about the claims count and severity distributions. The actuary may not be comfortable in making these ruin assumptions. Instead, he or she may generate such distributions by running extensive computer simulations of corporate models, I introduce a method to reduce the number of simulations necessary' to estimate the 1 and 0.1 percentiles of the surplus distribution. This approach 'cuts off' the tail at approximately the tenth percentile of the sample distribution and generates new tails for the distribution by resampling. Averages of the new order statistics approximate the I and 0.1 percentiles.

Description: This paper demonstrates the calculation of the moments of the distribution of aggregate life insurance claims from seriatim inforce data, assuming that each record represents an independent Bernoulli trial with its own known probability of a claim, q. Continuous distributions matching the first three or four moments are identified.

Description: Sooner or later a casualty actuary is confronted by the question, Given a history of paid loss amounts by calendar year, what should reserves be? Often, it is not possible to accurately gather and analyze additional data within the time constraints for the reserving decision. The algebraic reserving method presented in this paper offers one approach to rapidly addressing this problem. The paper consists of four sections - General Considerations, Formulas, Examples, and Conclusion.

Description: A contingency table is a set of counts or frequencies obtained by classifying observations in two or more different ways. Log-linear analysis is applied to disability terminations, linking them to variables such as sex, age, region and maximum benefit period. Application to risk classification and underwriting are outlines.

Description: In this paper we shall present our results in terms of the estimation of human mortality rates, but the results carry over to other applications. We shall discuss a Bayesian model that encompasses both graduation [smoothing] and prediction.

Description: In this paper, we illustrate how to value American-style options using the Least-Squares Monte Carlo LSM approach proposed by Longstaff and Schwartz 2001 and investigate whether there exists an optimal regression complexity in the LSM framework for options pricing. In particular, we use the smoothing spline in the regression step, which allows us to control the regression complexity on a continuous scale with just one tuning parameter. Numerical results on American put options indicate that we need to use more than a linear regression, but as the regression becomes more complex, the accuracy of the LSM method quickly deteriorates. From 39th Actuarial Research Conference.

Description: In Volume LXXV of the Proceedings there appeared a paper entitled Risk Loads for Insurers by Feldblum. Confidence intervals for the betas in TABLE 4 [Profit Margins and Their Standard Deviations by Line of Business] of this paper can be generated using the assumption of underlying normal distributions. However, bootstrapping operational or not for interval estimates does not require the normality assumption. The method of operational bootstrapping does not use random numbers. The method for the 4-dimensional case, used to generate the interval estimates in the current paper, is a natural generalization of the bivariate case. I use operational bootstrapping to generate interval estimates for Betas shown in the TABLE 5.

Description: This paper illustrates the application of stochastic control methods in managing the risk associated with an insurance business. We present the Hamilton-Jacobi-Bellman HJB equation and demonstrate its use in finding the optimal investment strategy based on some given criteria. Here we consider an insurance business with a fixed amount available for investment in a portfolio consisting of one non-risky asset and one risky asset. The object of the resulting control problem is to determine the investment strategy that minimizes infinite time ruin probability. The existence of a solution to the resulting HJB equation is shown. The relevant verification lemma is not presented in this paper and a numerical algorithm is given instead. Examples applied to exponential claims are also presented.