Coherent Modeling and Forecasting of Mortality Patterns for Subpopulations Using Multiway Analysis of Compositions: An Application to Canadian Provinces and Territories

Mortality levels for subpopulations, such as countries in a region or provinces within a country, generally change in a similar fashion over time, as a result of common historical experiences in terms of health, culture, and economics. Forecasting mortality for such populations should consider the correlation between their mortality levels. In this perspective, we suggest using multilinear component techniques to identify a common time trend and then use it to forecast coherently the mortality of subpopulations. Moreover, this multiway approach is performed on life table deaths by referring to Compositional Data Analysis (CoDa) methodology. Compositional data are strictly positive values summing to a constant and represent part of a whole. Life table deaths are compositional by definition because they provide the age composition of deaths per year and sum to the life table radix. In bilinear models the use of life table deaths treated as compositions generally leads to less biased forecasts than other commonly used models by not assuming a constant rate of mortality improvement. As a consequence, an extension of this approach to multiway data is here presented. Specifically, a CoDa adaptation of the Tucker3 model is implemented for life table deaths arranged in three-dimensional arrays indexed by time, age, and population. The proposed procedure is used to forecast the mortality of Canadian provinces in a comparative study. The results show that the proposed model leads to coherent forecasts.     

Modeling Mortality With Jumps: Applications to Mortality Securitization

In this article, we incorporate a jump process into the original Lee–Carter model, and use it to forecast mortality rates and analyze mortality securitization. We explore alternative models with transitory versus permanent jump effects and find that modeling mortality via transitory jump effects may be more appropriate in mortality securitization. We use the Swiss Re mortality bond in 2003 as an example to show how to apply our model together with the distortion measure approach to value mortality-linked securities. Pricing the Swiss Re mortality bond is challenging because the mortality index is correlated across countries and over time. Cox, Lin, and Wang (2006) employ the normalized multivariate exponential tilting to take into account correlations across countries, but the problem of correlation over time remains unsolved. We show in this article how to account for the correlations of the mortality index over time by simulating the mortality index and changing the measure on paths.     

Mind the Gap: A Study of Cause-Specific Mortality by Socioeconomic Circumstances

Socioeconomic groups may be exposed to varying levels of mortality; this is certainly the case in the United Kingdom, where the gaps in life expectancy, differentiated by socioeconomic circumstances, are widening. The reasons for such diverging trends are yet unclear, but a study of cause-specific mortality may provide rich insight into this phenomenon. Therefore, we investigate the relationship between socioeconomic circumstances and cause-specific mortality using a unique dataset obtained from the U.K. Office for National Statistics. We apply a multinomial logistic framework; the reason is twofold. First, covariates such as socioeconomic circumstances are readily incorporated, and, second, the framework is able to handle the intrinsic dependence amongst the competing causes. As a consequence of the dataset and modeling framework, we are able to investigate the impact of improvements in cause-specific mortality by socioeconomic circumstances. We assess the impact using (residual) life expectancy, a measure of aggregate mortality. Of main interest are the gaps in life expectancy among socioeconomic groups, the trends in these gaps over time, and the ability to identify the causes most influential in reducing these gaps. This analysis is performed through the investigation of different scenarios: first, by eliminating one cause of death at a time; second, by meeting a target set by the World Health Organization (WHO), called WHO 25 × 25; and third, by developing an optimal strategy to increase life expectancy and reduce inequalities.     

Modeling Period Effects in Multi-Population Mortality Models: Applications to Solvency II

Recently Cairns et al. introduced a general framework for modeling the dynamics of mortality rates of two related populations simultaneously. Their method ensures that the resulting forecasts do not diverge over the long run by modeling the difference in the stochastic factors between the two populations with a mean-reverting autoregressive process. In this article, we investigate how the modeling of the stochastic factors may be improved by using a vector error correction model. This extension is highly intuitive, allowing us to visualize the cross-correlations and the long-term equilibrium relation between the two populations. Another key benefit is that this extension does not require the user to assume which one of the two populations is dominant. This benefit is important because, as we demonstrate, it is not always easy to identify the dominant population, even if one population is much larger than the other. We illustrate our proposed extension with data from a pair of populations and apply it to the calculation of Solvency II risk capital.     

The CBD Mortality Indexes: Modeling and Applications

Most extrapolative stochastic mortality models are constructed in a similar manner. Specifically, when they are fitted to historical data, one or more series of time-varying parameters are identified. By extrapolating these parameters to the future, we can obtain a forecast of death probabilities and consequently cash flows arising from life contingent liabilities. In this article, we first argue that, among various time-varying model parameters, those encompassed in the Cairns-Blake-Dowd (CBD) model (also known as Model M5) are most suitably used as indexes to indicate levels of longevity risk at different time points. We then investigate how these indexes can be jointly modeled with a more general class of multivariate time-series models, instead of a simple random walk that takes no account of cross-correlations. Finally, we study the joint prediction region for the mortality indexes. Such a region, as we demonstrate, can serve as a graphical longevity risk metric, allowing practitioners to compare the longevity risk exposures of different portfolios readily.     

组合预测模型在货运量预测中的应用

本文对灰色预测模型和ARIMA预测模型进行组合,建立了组合模型,并应用于货运量的预测,实证预测表明,组合模型的预测精度优于单一的预测模型,预测结果与实际货运量拟合较好。     

基于ARCH类模型的VaR方法在外汇风险计量中的应用

本文将残差项服从t分布的ARCH类模型应用于我国外汇风险的计量。通过美元/人民币汇率日波动率VaR值的实证分析发现:(1)ARCH类模型预测得到的VaR值都能很好地拟合美元/人民币汇率日波动率的实际情况,美元/人民币汇率存在明显的ARCH效应;(2)基于ARCH类模型预测的VaR值其计算精度基本上都超过了J.P.Morgan公司RiskMetrics所采用的EWMA模型,这验证了本文选取ARCH类模型以及考虑残差项服从t分布的合理性;(3)ARCH类模型中以TARCH-M(1,1)模型计算结果最为理想。本研究可为金融机构、监管部门以及外汇投资者规避外汇风险提供决策依据和理论参考。     

Mortality Inequality in England over the Past 20 Years*

In this paper, we study the evolution of age‐group‐ and gender‐specific mortality and mortality inequality in England between 2003 and 2016, by comparing small geographic areas ranked by deprivation and grouped into bins of similar population size. We show that across all age groups, but especially in the older age groups (65+), there has been a clear and significant reduction in rates of mortality since 2003. In spite of these improvements, we continue to see significant inequalities in mortality across most age groups in 2016 and evidence of rising inequalities among women in the 65+ and men in the 80+ age groups. Furthermore, we see a striking stalling of the downwards trend in mortality and mortality inequality observed between 2003 and 2010 during the years of economic austerity in the aftermath of the 2008 financial crisis in England between 2010 and 2016. Analysis of specific causes of death among adults aged 20–79 allows us to examine the drivers and dynamics of these trends in more depth, as well as to consider scope for, and types of, interventions that would be appropriate at different ages.     

Forecasting and Arbitrage of the Nikkei Stock Index Futures: An Application of Backpropagation Networks

A neural network model was used in forecasting the basis in SIMEX Nikkei Stock Index futures. Results for out of sample show that the neural network forecast performance was better than that of the ARIMA model. Also, a two-way ANOVA confirms that the employed neural network was able to provide the trader with more arbitrage profits than the traditional cost-of-carry model even though it observed relative less profitable arbitrage timing. The results can be attributed to the network';s higher ability to capture nonlinear market patterns.     

Stochastic Mortality Modeling: Key Drivers and Dependent Residuals

This article proposes an alternative framework for modeling the stochastic dynamics of mortality rates. A simple age basis combined with two stochastic period factors is used to explain the key mortality drivers, while the remaining structure is modeled via a multivariate autoregressive residuals model. The latter captures the stationary mortality dynamics and introduces dependencies between adjacent age-period cells of the mortality matrix that, among other things, can be structured to capture cohort effects in a transparent manner and incorporate across ages correlations in a natural way. Our approach is compared with models with and without a univariate cohort process. The age- and period-related latent states of the mortality basis are more robust when the residuals surface is modeled via the multivariate time-series model, implying that the process indeed acts independently of the assumed mortality basis. Under the Bayesian paradigm, the posterior distribution of the models is considered to explore coherently the extent of parameter uncertainty. Samples from the posterior predictive distribution are used to project mortality, and an in-depth sensitivity analysis is conducted. The methodology is easily extendable in multiple ways that give a different form and degree of significance to the different components of mortality dynamics.     

英国特许公认会计师公会执业监管制度及其启示

本文介绍了ACCA执业监管的具体做法 ,从中得到启示 ,执业监管的出发点和归宿点应是帮助和督促会计师事务所完善审计程序 ,提高审计质量 ,降低审计风险 ;执业监管内容及程序应视被监管对象的规模和类型而有所不同 ;高素质专职检查队伍有利于提高执业监管质量和效率。     

Forecasting,rational expectations and the phillips-curve: An empirical investigation

The rational-expectations version of the Phillips-curve is empirically evaluated for Switzerland using a wide variety of specifications. It turns out that the results are highly sensitive to measurement of both the natural rate and expectations of nominal variables. No reliable Phillips-curve seems to exist. In addition, information on the relative quality of different forecasting schemes is obtained for a number of important macroeconomic variables.     

Modeling Frost Losses: Application to Pricing Frost Insurance

The main objective of this article is to model the losses caused by frost events and use it to price frost insurance. Since the data on frost events are either unavailable or rarely available, we have chosen to obtain a model for frost losses based on temperature by using some fundamental agricultural engineering findings on frost damage. The main challenges in modeling frost loss variables are, first, the nonlinearity of the frost losses with respect to the temperature and, second, the fruit resistance to the first few hours of low temperature. We address both issues when introducing our frost loss variable. Then after finding the loss model, we use it to price frost insurance for a general family of insurance contracts that do not generate any risk of moral hazard. In particular, we will find the premiums of stop-loss policies for losses to citrus fruits using Value at Risk, Conditional Value at Risk, and Wang's premium based on temperature data from San Joaquin Drainage in California.     

Modeling and Pricing Longevity Derivatives Using Stochastic Mortality Rates and the Esscher Transform

The Lee-Carter mortality model provides a structure for stochastically modeling mortality rates incorporating both time (year) and age mortality dynamics. Their model is constructed by modeling the mortality rate as a function of both an age and a year effect. Recently the MBMM model (Mitchell et al. 2013) showed the Lee Carter model can be improved by fitting with the growth rates of mortality rates over time and age rather than the mortality rates themselves. The MBMM modification of the Lee-Carter model performs better than the original and many of the subsequent variants. In order to model the mortality rate under the martingale measure and to apply it for pricing the longevity derivatives, we adapt the MBMM structure and introduce a Lévy stochastic process with a normal inverse Gaussian (NIG) distribution in our model. The model has two advantages in addition to better fit: first, it can mimic the jumps in the mortality rates since the NIG distribution is fat-tailed with high kurtosis, and, second, this mortality model lends itself to pricing of longevity derivatives based on the assumed mortality model. Using the Esscher transformation we show how to find a related martingale measure, allowing martingale pricing for mortality/longevity risk–related derivatives. Finally, we apply our model to pricing a q-forward longevity derivative utilizing the structure proposed by Life and Longevity Markets Association.     

Inflation Differentials between Spain and the EMU: A DSGE Perspective

This paper estimates a dynamic stochastic general equilibrium model of a currency union with nominal rigidities to explain the sources of inflation differentials between the Economic Monetary Union (EMU) and one of its member countries, Spain. The paper finds that productivity shocks account for 85% of the variability of the inflation differential. Demand shocks explain a large fraction of output growth volatility but not variability in inflation differentials. In addition, the estimated model finds evidence that inflation dynamics are different across countries in the nontradable sector only. Finally, the Balassa–Samuelson effect does not appear to be an important driver of the inflation differential during the EMU period.     

Application of Relational Models in Mortality Immunization

The prediction of future mortality rates by any existing mortality models is hardly exact, which causes an exposure to mortality (longevity) risk for life insurers (annuity providers). Since a change in mortality rates has opposite impacts on the surpluses of life insurance and annuity, hedging strategies of mortality and longevity risks can be implemented by creating an insurance portfolio of both life insurance and annuity products. In this article, we apply relational models to capture the mortality movements by assuming that the realized mortality sequence is a proportional change and/or a constant shift of the expected one, and the size of the changes varies in the length of the sequences. Then we create a variety of non-size-free matching strategies to determine the weights of life insurance and annuity products in an insurance portfolio for mortality immunization, where the weights depend on the sizes of the proportional and/or constant changes. Comparing the hedging performances of four non-size-free matching strategies with corresponding size-free ones proposed by Lin and Tsai, we demonstrate with simulation illustrations that the non-size-free matching strategies can hedge against mortality and longevity risks more effectively than the size-free ones.     

美国通胀中的货币及非货币因素——变化趋势及在预期中的运用

上世纪80年代以来,美国经济和金融市场的一系列结构性长期变化使货币因素和通胀之间的稳定关系逐渐疏远,通胀不再总是货币现象;其中的关键变化是货币流通速度波动加大并趋势性下降,使货币供给与名义GDP及价格水平关系的稳定性和可预期性下降。未来影响美国通胀的主要因素是总供给和总需求的关系特别是消费者支出的动态变化。     

解释结构模型在投入产出表结构分析中的应用

利用投入产出表中的投入产出关系,分析研究各产业部门结构,在此基础上建立投入产出解释结构模型,并利用模型对河南省1987、1992、1997年投入产出表中的各工业产业部门进行实证研究,可以找出河南省在此期间的一些基础工业部门.     

人工智能在英美央行中的应用及思考

随着人工智能技术的发展应用,越来越多金融机构推出了智能客服、智能投顾等服务,在这一发展趋势下,金融业务逐渐互联网化,同时,传统的金融监管手段已经无法满足日益复杂的监管需求。本文从英格兰银行和美联储关于人工智能技术在金融监管领域的应用研究现状着手,总结其应用研究过程中的局限性,反思我国央行应用研究中存在的不足并提出监管意见。