Description: Transcript of the Q&A period from Session 6A: Projection and Statistical Modeling of Mortality at Late Age

Description: In this paper, we investigate the dynamics of the Lee-Carter mortality index parameter kt. Specifically, we perform statistical hypothesis tests to examine whether the mortality indexes for Canada, England and Wales and the United States are best described by stochastic trends difference stationary models or deterministic trends trend stationary models. The empirical results favor broken-trend stationary models over difference stationary models, which are used in most previous applications of the Lee-Carter method. The results also give strong statistical evidence that the rates of mortality decline for the three populations have significantly accelerated in mid-1970s.

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 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: 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: In this note, the asymptotic behavior of the probability of ruin is derived by means of infinitesimal generators and Laplace transforms. Using these same tools, it is shown that the probability of ruin has an algebraic decay rate if the insurance company invests its capital in a risky asset with a price which follows a geometric Brownian motion. The latter result is shown to be valid not only for exponentially distributed claim amounts, as in Frolova et al. 2002, but, more generally, for any claim amount distribution that has a moment generating function defined in a neighborhood of the origin.

Description: After reading the Panjer-Bellhouse paper in the Proceedings of the Ball State University Conference, I wondered whether their technique could be used when a realistic investment process was assumed. I believe that such an extension is necessary if the theory is to have any practical application I have had little success in trying to do this. I have decided to present some thoughts and to invite others with different perspectives to bring them to fruition.

Description: This paper, originally published in 1992 in the Transactions of Society of Actuaries Vol. 44, deals with a topic that is becoming increasingly important to actuaries in most fields of practice. “Without relying on formulas, this paper presents the important concepts underlying the theory of arbitrage-free pricing of interest-rate-contingent cash flows.” This paper, by James A. Tilley, won the 1992-93 Annual Prize, and the Halmstad Prize for 1992. The paper includes written discussion and the author’s review of the discussions.

Description: We propose asymptotically correct two-sided bounds for random sums where the number of summands has an arbitrary distribution which can be viewed as ruin probabilities or accumulated claim sizes in various risk processes. The bounds are fairly new and they reveal the real accuracy of some well-known and widely used asymptotic formulas. It turns out that this accuracy can be poor and the range where these formulas give appropriate approximations depends on the shape of the tail distribution of the summands. This dependence is examined in the research.

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.