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

Description: A discussion of the possible effort required and impacts resulting from the implementation of C3 Phase II for establishing risk-based capital for variable annuities. This article will describe practical considerations gleaned from actual valuation calculations recently performed by a consulting firm.

Description: In December 2007, Goldman Sachs launched a product called QxX index swap, which is designed to allow market participants to hedge or gain exposure to longevity and mortality risks. This presentation offers a quantitative analysis of this brand new financial innovation. First of all, the presentation sets up a risk-neutral framework to price QxX index swaps. This framework, which is based on the dynamics of death rates under a two-factor stochastic mortality model in a risk-adjusted probability measure, yields prices [spreads] that are fairly close to the spreads that Goldman Sachs currently offers. The presentation then explores the uncertainty involved in this model-based pricing framework. Specifically, it studies parameter risk by using Markov Chain Monte Carlo [MCMC] and model risk by examining structural changes in mortality dynamics. The results indicate that both model risk and parameter risk are significant. Actuaries should therefore be aware of these issues when placing a value on a longevity index swap.

Description: This presentation is a panel discussion, session number 9PD, from the 2000 Valuation Actuary Symposium, held September 14-15 in Washington, DC. A fundamental assumption in stochastic asset/liability modeling is the underlying economic scenario generator. In this session the panelists discuss various scenario generation techniques, assumptions underlying bond and equity scenario generators, and choosing suitable economic scenario generators for different applications. Discussion from participants is included.

Description: In the present paper, we propose and investigate a numerical method of computing the probability distribution of S. Inversion of the Laplace transform moment generating function is shown to be a better approach than the existing recursive method for find the distribution of sum of several independent random variables. In the continuous case, in many situations, numerical inversion needs to be used to compute the probability distribution function of the sum.

Description: This paper addresses the stochastic modeling for managing asset liability process. We start with developing a jump-diffusion process for evaluating of the liabilities of the insurance company in general. We then formulate the ALM process into a stochastic control problem. With this approach, we present a Bel|man-Dreyfus Fundamental type formula for ALM process in terms of the solution of a system of algebraic equations and partial differential equations.

Description: One of the most important problems in Finance is the valuation of financial securities written on underlying assets whose prices are subject to uncertainty. This paper presents a technique to estimate the unknown stochastic volatilities by solving the inverse problem associated with the parabolic partial differential equation governing risk neutral derivative security prices. This technique can be applied in a very general multi-factor setting and numerical examples are provided.

Description: Discussion of the movement toward principle-based reserves for LTC insurance.

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.

Description: This paper introduces a new direction for evaluating numerically survival probabilities pointed out by H. Seal in his book ‘Survival Probabilities: The goal of Risk Theory’. Some of special cases can be considered as a weighted Poisson process with an infinitely divisible mixing distribution. This property is well known for the negative binomial case [gamma mixing distribution].