Description: In this paper we study the pricing of financial options and contingent claims. We show that two time-honored concepts in actuarial science - the Esscher transform and the adjustment coefficient - are efficient tools for pricing many options and derivative securities if the logarithms of the prices of the primitive securities are certain stochastic processes with stationary and independent increments. We also study the pricing of American options on two stocks without expiration date and with payoff functions which are homogeneous with respect to the two stock prices.

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: The two-parameter Pareto distribution is a commonly used model in reliability and risk modeling. Minimum variance unbiased estimates of the parameters of Pareto distribution are not known. In this paper, we propose and investigate a method of estimation of the parameters of the Pareto distribution. This method is based on minimization of the Kolmogorov-Smirnov distance between the empirical cumulative distribution function [cdf] and the cdf of the Pareto distribution.

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: 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: The investment risk generated by a stochastic interest rate is recognized as often the greatest risk associated with a whole life or retirement policy. Recent research has investigated the mathematics of this risk when the interest rate follows a stochastic process and the time to death is considered to be random. In this paper we focus on the use of the zero coupon bond as an investment instrument to fund a whole life policy. It is unlikely that a company will entirely fund a particular single policy with a zero coupon bond.

Description: This paper presents the modeling of mortality risk from exposure to a potential future extreme event such as a natural disaster and a terrorist attack, and its impact on life insurance. With this new model, quantities associated with the total force of mortality such as survival function are derived and the impact of mortality risk on life insurance is examined.

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 is a study on the Nesbitt formula and the variants to this formula.