A State-Space Estimation of the Lee-Carter Mortality Model and Implications for Annuity Pricing

In this article we investigate a state-space representation of the Lee-Carter model which is a benchmark stochastic mortality model for forecasting age-specific death rates. Existing relevant literature focuses mainly on mortality forecasting or pricing of longevity derivatives, while the full implications and methods of using the state-space representation of the Lee-Carter model in pricing retirement income products is yet to be examined. The main contribution of this article is twofold. First, we provide a rigorous and detailed derivation of the posterior distributions of the parameters and the latent process of the Lee-Carter model via Gibbs sampling. Our assumption for priors is slightly more general than the current literature in this area. Moreover, we suggest a new form of identification constraint not yet utilised in the actuarial literature that proves to be a more convenient approach for estimating the model under the state-space framework. Second, by exploiting the posterior distribution of the latent process and parameters, we examine the pricing range of annuities, taking into account the stochastic nature of the dynamics of the mortality rates. In this way we aim to capture the impact of longevity risk on the pricing of annuities. The outcome of our study demonstrates that an annuity price can be more than 4% under-valued when different assumptions are made on determining the survival curve constructed from the distribution of the forecasted death rates. Given that a typical annuity portfolio consists of a large number of policies with maturities which span decades, we conclude that the impact of longevity risk on the accurate pricing of annuities is a significant issue to be further researched. In addition, we find that mis-pricing is increasingly more pronounced for older ages as well as for annuity policies having a longer maturity.Comment: 9 pages; conference pape

A unified approach to mortality modelling using state-space framework: characterisation, identification, estimation and forecasting

This paper explores and develops alternative statistical representations and estimation approaches for dynamic mortality models. The framework we adopt is to reinterpret popular mortality models such as the Lee-Carter class of models in a general state-space modelling methodology, which allows modelling, estimation and forecasting of mortality under a unified framework. Furthermore, we propose an alternative class of model identification constraints which is more suited to statistical inference in filtering and parameter estimation settings based on maximization of the marginalized likelihood or in Bayesian inference. We then develop a novel class of Bayesian state-space models which incorporate apriori beliefs about the mortality model characteristics as well as for more flexible and appropriate assumptions relating to heteroscedasticity that present in observed mortality data. We show that multiple period and cohort effect can be cast under a state-space structure. To study long term mortality dynamics, we introduce stochastic volatility to the period effect. The estimation of the resulting stochastic volatility model of mortality is performed using a recent class of Monte Carlo procedure specifically designed for state and parameter estimation in Bayesian state-space models, known as the class of particle Markov chain Monte Carlo methods. We illustrate the framework we have developed using Danish male mortality data, and show that incorporating heteroscedasticity and stochastic volatility markedly improves model fit despite an increase of model complexity. Forecasting properties of the enhanced models are examined with long term and short term calibration periods on the reconstruction of life tables.Comment: 46 page

Improved surgical technique for the establishment of a murine model of aortic transplantation.

Aortic allotransplantation is a reliable procedure to study the evolvement of chronic rejection in mice. The progressive nature of this process in mice is characterized by diffuse and concentric myointimal proliferation which is inevitably associated with variable degrees of luminal constriction. These vascular changes are comparable to those that are witnessed in organ allografts undergoing chronic rejection in humans, underscoring its utility as a model of choice for the study of the development of this lesion. Whilst improved surgical technique has resulted in markedly enhanced graft survival, the results are far from being acceptable. Realizing this limitation, we embarked on developing a modified technique for aortic transplantation which would allow for improved graft survival in mice. A bypass conduit was created by end-to-side anastomosis of a segment of the donor's thoracic aorta into the infrarenal portion of the recipient's abdominal aorta. Using this technique, the graft survival was >98% with evidence in allotransplanted aorta of morphological changes pathognomonic of chronic rejection. On the contrary, no histopathological anomalies were discerned in aortic grafts transplanted across syngeneic animals. This modified surgical approach ameliorates the unacceptably high graft loss associated with earlier techniques, further extending the utility of this model as a tool to study the molecular and cellular mechanisms rudiment to the evolvement of chronic rejection

Linear theory of active control of pressure oscillations in combustion chambers

Active control of longitudinal pressure oscillations in combustion chambers has been studied theoretically using a digital state-feedback control technique. The formulation is based on a generalized wave equation which accommodates various influences on combustion, mean flow, unsteady motions, and contol actions. After a procedure equivalent to the Galerkin method, a system of ordinary differential equation governing the amplitude of each oscillatory mode is derived, serving as a basis for the controller design. The control actions is provided by a finite number of point acutators, with the instantaneous chamber conditions monitored by a few sensors. Several important control aspects such as sampling period, locations of sensors and controllers, controllability and observabi1ity have been investigated. As a specific example, the case involving two controlled and two residual (uncontrolled) modes is studied. The control and observation spillover phenomena due to the residual modes are clearly demonstrated

Improving an interactive simulator for computer systems with learning objects

In the 21st century, learning is a crucial activity through which people can assimilate or acquire new knowledge. However, many existing e-Iearning systems contain complicated knowledge structure that hinders the reuse or sharing of knowledge. In a previous project awarded by the Microsoft Research Asia, we successfully developed an interactive simulator to facilitate the learning of essential concepts related to computer systems through live animations. Here, we propose to integrate learning objects and relevant technologies into our interactive simulator to illustrate the underlying knowledge structure and, more importantly, facilitate the sharing and reuse of relevant concepts. Through adopting the IEEE learning object metadata (LOM) standard, our simulator can easily exchange relevant learning objects with other e-Iearning systems. The system design and prototype implementation of our LOM-based simulator is considered in this paper to evaluate how general and experienced users can benefit from our LOM-based simulator in various ways. © 2010 IEEE.published_or_final_versionThe 2nd International Conference on Education Technology and Computer (ICETC 2010), Shanghai, China, 22-24 June 2010. In Proceedings of the International Conference on Education Technology and Computer, 2010, v. 3, p. 16-2