Description: Applications of Lagrangian distributions to modelling claim frequency data in an insurance portfolio is a relatively new concept. The major difficulty is that the generating functions of these distributions cannot be expressed in terms of elementary functions. Also deriving moments and/or cumulants is somewhat tedious. This article illustrates how to use Maple effectively to overcome these difficulties.

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: 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 this paper, we derive three important longevity Greeks on the basis of an extended version of the Lee-Carter model that incorporates stochastic volatility.

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: In a series papers by Willmot and Lin, both exponential and non-exponential bounds for the tail probability of various compound distributions have been derived. In Wilmot, it was suggested that non-exponential bounds for the ruin probability were difficult to obtain using martingale arguments. In this note, we show how to use martingale inequalities to obtain some upper bounds for the ruin probability.

Description: This paper builds a new risk model for a firm which is sensitive to its credit quality. A modified Jarrow, Lando and Turnball model [Markov Chain model] is used to model the credit rating. Recursive equations for finite time ruin probability and distribution of ruin time are derived. Coupled Volterra type integral equation systems for ultimate ruin probability, severity of ruin and joint distribution of surplus before and after ruin are also obtained. Some numerical results are included.

Description: This paper presents a new methodology for obtaining fast algorithms and closed form solutions for pricing callable bonds in continuous time models. Results are directly applicable to regulatory scenario testing, immunization and market value accounting.

Description: In this paper we discuss some properties of the nth stop-loss order and their application in risk premium principles. We give a necessary condition and a sufficient condition for nth stop-loss orders. They are convenient tools to construct risk pairs with nth stop-loss orders. We show that exponential premium principles can diferentiate between losses more finely than the net premium principles under some conditions.

Description: Following Jorgensen and Paes De Souza 1994, Tweedie's compound Poisson distribution is fitted to private passenger automobile accident benefit data. The Tweedie process is a three parameter distribution which corresponds to a Poisson process for claim frequency with gamma distributed claim sizes. From Actuarial Research Conference 1995.