Description: In this paper, a mathematical model is constructed to study the deviations of claims, investment performance, operating expenses, and lapse expenses as random stochastic processes. Discussions of the paper submitted by 2 readers follows

Description: Discussion of how to obtain tight upper and lower bounds on E[hX] for a given function h, and a random variable X with three known moments.

Description: This paper presents an introduction to collective risk theory. In collective risk theory one seeks to investigate directly the risk enterprise as a whole. Primary interest is focused not upon the gains, losses, or claims from individual policies but upon the amount of total claims or the total gain arising from all the policies in the portfolio considered. Followed by several discussion papers submitted.

Description: The series expansion of a probability density function, known to actuaries by Esscher's name and to statisticians as the saddlepoint approximation, typically gets integrated to approximate probability values under the density, with a location parameter in the expansion chosen to optimize convergence of the integrated series. We review the general form, the accuracy and the derivation of the Esscher approximation. Then we propose using related series expansions for the derivative of a probability density function to approximate the value of the point of maximum likelihood for the density. The key is to make the value of the location parameter an unknown and assume it to be the point of maximum likelihood, which leads to a tractable optimization problem to find its value.

Description: The CSTEP 'Cluster Sampling for Tail Estimation of Probability' system is a desktop-based application to assist actuaries in efficient stochastic modeling through the implementation of Representative Scenario approaches. Its goal is to provide actuaries with an open-source HPC 'High Performance Computation' research platform to select a sample set of representative 'pivot' risk scenarios through user-specified or user-researched distance definitions.

Description: Without relying on formulas, this paper presents the important concepts underlying the theory of arbitrage-free pricing of interest-rate-contingent cash flows: absence of opportunities for riskless arbitrage, completeness of markets, relative prices that do not depend on individual investors' subjective views or risk preferences, and expected-value pricing in the risk-neutral world. Using these concepts, the paper then describes the steps required to build continuous stochastic models of interest rates, including models that are either partially or fully arbitrage free.

Description: Several previous papers treat the rate of interest as a stochastic process in the determination of values of insurances and annuity functions. None of these papers consider the current interest rate as a starting point in the model. In this paper, autoregressive interest models, which are conditional upon current and past interest rates, are developed. It is shown how these models may be applied to the evaluation of moments of interest, insurance and annuity functions. Numerical results are also given.

Description: Survey of appointed actuaries about asset adequacy testing techniques currently being used in 2012.