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: From a session at the Spring meeting of the Society of Actuaries held in San Antonio, Texas, June 14-15, 2004 This session discusses emerging capital and reserve requirements on Variable annuities with guaranteed benefits and the effect that hedging/capital management strategies can have.

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: Presentation from the 41st Actuarial Research Conference held in August, 2006 in Montreal. This presentation extends the traditional Sparre Anderson model of ruin theory, using an Erlang distribution for inter-claim times and geometric Brownial motion for asset returns.

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 purpose of this discussion is to introduce a few additional points and discuss how different assumptions will alter the results in some cases.

Description: Discusses methods to efficiently run stochastic models in light of AG 43.

Description: Modeling experience sharing by David Yu who leads the retirement product and asset model development team within Prudential Financial

Description: This paper illustrates a current approach to capital allocation, referred to herein as Tail Contribution Analysis TCA, using it to evaluate the impact of changes in an insurer’s operations by allocating capital to individual lines of business. It then highlights a common problem in the implementation of the procedure arising from reserve volatility and briefly notes the failure of the methodology to account for a firm’s changing levels of risk under various strategies. Finally, it introduces an alternative method for analyzing business segments and strategies called Economic Profit Analysis EPA. We will discuss EPA’s key feature, “volatility replication,” an intuitively appealing process of building investor expectations and capital market information into the risk-and-return measurements used to evaluate strategic decisions. Finally, we will illustrate the benefit of using EPA in overcoming the problems of TCA and thereby providing concise reliable information for business decision making.

Description: This paper introduces a rich stochastic modeling framework for understanding risks in multiple-decrement contracts. The example in the paper is a 20-year Term insurance contract. Not only are mortality and lapsation considered stochastic, but the parameters governing them are. For example, mortality risk is composed of four risk elements, including error generated in the underwriting process, volatility around the best estimate, catastrophic events that impact mortality, and the trend in mortality improvement or deterioration. When stochastically modeled, the relative contribution and risk profile of each risk element can be evaluated. Generating stochastic mortality results provides a distribution of results that an organization faces and the severity and incidence of the tail events.