Description: Discussion of Living to 100 Session 6A: Projection and Statistical Modeling of Mortality at Late Age

Description: Logistic-type models for the force of mortality like those introduced by Perks or Kannisto provide better fit to mortality data of people aged over 85 than Makeham’s model where the force of mortality increases exponentially with age. However, the difficulty in estimating their parameters by the maximum likelihood method makes their use less popular among actuaries. For Kannisto’s model, this paper proposes a weighted least-squares estimator which can easily be calculated with any regression software. The estimator is shown to be consistent, asymptotically unbiased and normally distributed. For Perks’ model, using a Taylor’s series expansion, the estimation problem is again reduced to a least-squares problem. The various estimators proposed in the paper are compared numerically using Canadian mortality data.

Description: This paper presents a model that projects withdrawal and investment returns for a hypothetical retirement account. From Retirement Needs Framework, M-RS00-1.

Description: This paper presents a multi-state stochastic model for analyzing continuing care retirement community CCRC populations. The model considers CCRCs with a number of independent living units and a skilled nursing facility. Residents may transfer temporarily or permanently to this facility. It is assumed that units vacated by deaths, withdrawals or permanent transfers are immediately occupied by new residents. Transfers are modeled using a time-homogeneous Markov process. The paper provides some probabilistic results and some numerical results obtained using this model. Some important generalizations of the model are also briefly discussed.

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.

Description: This paper discusses the theoretic framework of modeling captial markets: index-based composition methodology and statisical procedure of model construction and extension: wavelets-based financial signal processing technique. It also discusses the implications and applications, measuring the market uncertainty and volatility highlighting the S&P 500 as an example.

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: Presented at Living to 100 symposium, January 2011. This paper presents a method for using death records to infer exposure on non-extinguished cohorts, thereby allowing the development of a credible table for high ages.

Description: All claim reserve systems endeavor to derive estimates of the unpaid portion of claims which have been incurred over a given period of time, making use of information on numbers of claims and amounts paid on claims as of the valuation date. In this paper, a claim reserve system is described. While the system does produce the traditional type of single-point estimates of claim reserves, it also provides the user with frequency distributions of claim reserves

Description: The purpose of this note is to show how certain formulas of life contingencies can be derived almost painlessly under the uniform distribution of deaths assumption.