Description: The purpose of this paper is to survey some new results concerning the term structure of interest rates and discuss actuarial applications. The term structure of interest rates exhibits the relationship among the yields on default free debt instruments of different maturities. Although there is a considerable volume of literature dealing with the determinants of the term structure the analysis has until recently been presented for the most part in a deterministic i.e. non- stochastic framework. This constrasts with the treatment of capital assets where equilibrium prices have been obtained under the assumption that returns on these assets are random variables.

Description: This is a presentation from 43rd Actuarial Research Conference ARC, Regina, August 14–16, 2008. This talk will present the moment generating function of the discounted compound Poisson aggregate sums when the deflated claims are PH distributed and moment generating function of the discounted compound renewal sums.

Description: This is the abstract of the paper 'A Stochastic Definition of Future Shares'. The traditional definition of actuarial future values and stochastic definition of Ramsay are discussed. A modification of Ramsay's definition is proposed and an application to life insurance reserves is 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].

Description: An insurance company starts with an initial surplus, collects premium, pays claims to policyholders and pays dividends to stockholders. What remains is the following year’s surplus. The process continues. This paper describes how to calculate the distribution of surplus for any given year. With these distributions, one can make the calculations of premiums and dividends.

Description: Appendix to the Critical Review of Stochastic Simulation Literature and Applications for Health Actuaries. The Development of a Simulation Model of Primary Prevention Strategies for Coronary Heart Disease

Description: An Overview of Stochastic Simulation modeling techniques and usages

Description: In a stochastic world consideration of only a few deterministic scenarios can potentially be dangerous. The aim of the present research is to study the computation of the cost of mismatch using stochastic interest rate models instead of scenario testing. In this paper, two commonly used Stochastic interest rate models are considered: the one introduced by Vasicek 1977 and the one proposed by Cox, Ingersoll and Ross 1985.

Description: Random sum models with compound distributions are used extensively in modeling of insurance risks. Unfortunately, the compound distributions themselves are awkward to evaluate. Consequently, various numerical and analytical approximative techniques have been used. In this talk we derive various upper and lower bounds on the tails of compound distributions. Some notions in reliability theory are used.

Description: This paper presents a methodology of pricing the guaranteed minimum death benefit of a variable annuity in a market model with jumps. Recent developments in the stock market make variable annuities very attractive products from the insured point of view, but less attractive for insurers. The insured still has the possibility of investment benefits, while avoiding the risk of a stock market collapse. The insurer wants to minimize its risk and yet sell a competitive product. The financial market model consists of one riskless asset and one risky asset whose price jumps in proportions J at some random times T which correspond to the jump times of a Poisson process. The model describes incomplete markets and there is no perfect hedging. In the second part of the paper, we describe a possible method of risk analysis for binomial tree models.