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

Pricing and risk management of long dated products in finance and insurance

Population ageing has presented new challenges and opportunities for insurance companies to address the increasing demand of products that are designed for the purpose of financing retirement. A change of pricing, modelling and risk management approach is required for insurers that are engaged in offering long term policies for retirement. This thesis addresses several pricing and risk management problems of long dated contracts from a supplier's perspective. The thesis begins with a study of market-based longevity risk management for a hypothetical life annuity portfolio subjected to longevity risk. Prices of longevity swaps and caps are derived analytically under a tractable Gaussian mortality model. Various hedging features exhibited by an index-based longevity swap and a cap are demonstrated with respect to different assumptions on the market price of longevity risk, the term to maturity of the hedging instruments and the size of the underlying annuity portfolio. Pricing and risk analysis of guaranteed lifetime withdrawal benefits embedded in variable annuities is studied next, with a focus on the interaction of equity and longevity risk. The guarantee is designed to protect policyholders from longevity risk and downside investment risk. It is priced using two approaches that are proved to be equivalent. Financial and longevity risks underlying the guarantee are quantified based on sensitivity and profit & loss analysis. Effectiveness of a static hedge of longevity risk is examined with respect to different levels of equity exposure. The benchmark approach, where the growth optimal portfolio is employed as the numeraire together with the real world probability measure as the pricing measure, is applied to investigate the pricing and hedging of long dated bonds. The thesis employs a tractable index model with stochastic interest rate to model the growth optimal portfolio. Non-parametric kernel-based technique is applied for parameter estimation. Closed-form expressions for bond prices and hedge ratios are derived under the real world probability measure. The thesis compares market prices of long dated bonds with model prices derived under the benchmark approach. A dynamic hedging strategy of long dated bonds is tested using empirical data

An investigation of the effectiveness of human resource management in the Hong Kong police

In the literature, there is the increasing trend to link human resource planning with strategic planning giving greater importance to, and greater involvement of, human resource management in organization strategy. Also the Hong Kong Police is a manpower oriented discipline force and the human resource management functions play a critical role in the effective management of these human resources. Therefore, the critical nature of the human resource management of the Hong Kong Police justifies a management report orientation where the focus is on the production of positive and practical recommendations. The objectives of the report are to evaluate the effectiveness of the existing human resource management system of the Hong Kong Police and also if and where appropriate to make recommendations designed to enhance the present system. In order to achieve the objectives, four aspects were evaluated. The first aspect is the human resource management goals of the Hong Kong Police. It was evaluated against the criteria of the extent to which it is consistent with the ii Vision, Statement of the Common Purposes and Values of the Police. The second aspect is its policies and practices of the each of the functions, which include 1. human resource planning (HRP), 2. recruitment and selection, 3. training and career development, 4. compensation and benefits management, 5. performance evaluation, 6. employee and labor relations, 7. counseling and 8. termination of the existing human resource management. It was evaluated through the comparison between the policies and practices of the each of the functions mentioned above and the corresponding theoretical functional goals. The third aspect is outcomes of human resource management, including complaints from the public, and opinions to it from the general public. It was evaluated against the overall goals of human resource management of the Hong Kong Police. The last but not the least, others, which are the things other than the above, factors viewed as relevant including what it has done during 1996 to 1999. Peters and Waterman Model was used as a framework for evaluating how well the Police was doing during this period. After considering all the aspects, we concluded that the Hong Kong Police did well in the planning process of the human resource management, as theoretically, the effectiveness of the human resource management was achieved. However, further improvement is needed in certain areas concerning the actual performance during the implementation, which may imply there are some problems that may affect the effectiveness of the human resource management of the Hong Kong Police. Based on the evaluation, we suggest that Competency Assessment Methods can be used as a framework for the Hong Kong Police to develop a set of competency for evaluating the performance of the employees. Also, a number of ways were suggested to improve the existing promotion mechanism. The supervisor’s recommendation involved in it can be improved by giving guidelines to the supervisors and having a group of supervisors to evaluate the performance of the employee. Also the recommendations should base on credible information. Moreover, feedback channels should be given to the employees to raise their opinions towards the decision in the promotion mechanism. In order to improve the competency of the supervisors, training should be given to strengthen their accountability for handling their work. Also a flexible and cafeteria benefits package was recommended to increase the flexibility of the existing benefits package iv for motivating the employees by giving autonomy to choose the benefits they need

Exogenous Expression of Human apoA-I Enhances Cardiac Differentiation of Pluripotent Stem Cells

The cardioprotective effects of high-density lipoprotein cholesterol (HDL-C) and apolipoprotein A1 (apoA-I) are well documented, but their effects in the direction of the cardiac differentiation of embryonic stem cells are unknown. We evaluated the effects of exogenous apoA-I expression on cardiac differentiation of ESCs and maturation of ESC-derived cardiomyocytes. We stably over-expressed full-length human apoA-I cDNA with lentivirus (LV)-mediated gene transfer in undifferentiated mouse ESCs and human induced pluripotent stem cells. Upon cardiac differentiation, we observed a significantly higher percentage of beating embryoid bodies, an increased number of cardiomyocytes as determined by flow cytometry, and expression of cardiac markers including α-myosin heavy chain, β-myosin heavy chain and myosin light chain 2 ventricular transcripts in LV-apoA-I transduced ESCs compared with control (LV-GFP). In the presence of noggin, a BMP4 antagonist, activation of BMP4-SMAD signaling cascade in apoA-I transduced ESCs completely abolished the apoA-I stimulated cardiac differentiation. Furthermore, co-application of recombinant apoA-I and BMP4 synergistically increased the percentage of beating EBs derived from untransduced D3 ESCs. These together suggests that that pro-cardiogenic apoA-I is mediated via the BMP4-SMAD signaling pathway. Functionally, cardiomyocytes derived from the apoA-I-transduced cells exhibited improved calcium handling properties in both non-caffeine and caffeine-induced calcium transient, suggesting that apoA-I plays a role in enhancing cardiac maturation. This increased cardiac differentiation and maturation has also been observed in human iPSCs, providing further evidence of the beneficial effects of apoA-I in promoting cardiac differentiation. In Conclusion, we present novel experimental evidence that apoA-I enhances cardiac differentiation of ESCs and iPSCs and promotes maturation of the calcium handling property of ESC-derived cardiomyocytes via the BMP4/SMAD signaling pathway

Hepatoprotective effects of berberine on carbon tetrachloride-induced acute hepatotoxicity in rats

Background: Berberine is an active compound in Coptidis Rhizoma (Huanglian) with multiple pharmacological activities including antimicrobial, antiviral, anti-inflammatory, cholesterol-lowering and anticancer effects. The present study aims to determine the hepatoprotective effects of berberine on serum and tissue superoxide dismutase (SOD) levels, the histology in tetrachloride (CCl 4)-induced liver injury.Methods: Sprague-Dawley rats aged seven weeks were injected intraperitoneally with 50% CCl 4 in olive oil. Berberine was orally administered before or after CCl 4 treatment in various groups. Twenty-four hours after CCl 4 injection, serum alanine aminotransferase (ALT) and aspartate aminotransferase (AST) activities, serum and liver superoxide dismutase (SOD) activities were measured. Histological changes of liver were examined with microscopy.Results: Serum ALT and AST activities significantly decreased in a dose-dependent manner in both pre-treatment and post-treatment groups with berberine. Berberine increased the SOD activity in liver. Histological examination showed lowered liver damage in berberine-treated groups.Conclusion: The present study demonstrates that berberine possesses hepatoprotective effects against CCl 4-induced hepatotoxicity and that the effects are both preventive and curative. Berberine should have potential for developing a new drug to treat liver toxicity. © 2010 Feng et al; licensee BioMed Central Ltd.published_or_final_versio

Genome-Wide Association Study of Hepatocellular Carcinoma in Southern Chinese Patients with Chronic Hepatitis B Virus Infection

One of the most relevant risk factors for hepatocellular carcinoma (HCC) development is chronic hepatitis B virus (HBV) infection, but only a fraction of chronic HBV carriers develop HCC, indicating that complex interactions among viral, environmental and genetic factors lead to HCC in HBV-infected patients. So far, host genetic factors have incompletely been characterized. Therefore, we performed a genome-wide association (GWA) study in a Southern Chinese cohort consisting of 95 HBV-infected HCC patients (cases) and 97 HBV-infected patients without HCC (controls) using the Illumina Human610-Quad BeadChips. The top single nucleotide polymorphisms (SNPs) were then validated in an independent cohort of 500 cases and 728 controls. 4 SNPs (rs12682266, rs7821974, rs2275959, rs1573266) at chromosome 8p12 showed consistent association in both the GWA and replication phases (ORcombined = 1.31–1.39; pcombined = 2.71×10−5–5.19×10−4; PARcombined = 26–31%). We found a 2.3-kb expressed sequence tag (EST) in the region using in-silico data mining and verified the existence of the full-length EST experimentally. The expression level of the EST was significantly reduced in human HCC tumors in comparison to the corresponding non-tumorous liver tissues (P<0.001). Results from sequence analysis and in-vitro protein translation study suggest that the transcript might function as a long non-coding RNA. In summary, our study suggests that variations at chromosome 8p12 may promote HCC in patients with HBV. Further functional studies of this region may help understand HBV-associated hepatocarcinogenesis