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| Author | : Laurent Callot |
| Publisher | : |
| Total Pages | : |
| Release | : 2014 |
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| Author | : Michael Sherris |
| Publisher | : |
| Total Pages | : 0 |
| Release | : 2011 |
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Modeling mortality and longevity risk presents challenges because of the impact of improvements at different ages and the existence of common trends. Modeling cause of death mortality rates is even more challenging since trends and age effects are more diverse. Despite this, successfully modeling these mortality rates is critical to assessing risk for insurers issuing longevity risk products including life annuities. Longevity trends are often forecasted using a Lee-Carter model. A common stochastic trend determines age-based improvements. Other approaches fit an age-based parametric model with a time series or vector autoregression for the parameters. Vector Error Correction Models (VECM), developed recently in econometrics, include common stochastic long-run trends. This paper uses a stochastic parameter VECM form of the Heligman-Pollard model for mortality rates, estimated using data for circulatory disease deaths in the United States over a period of 50 years. The model is then compared with a version of the Lee-Carter model and a stochastic parameter ARIMA Heligman-Pollard model. The VECM approach proves to be an improvement over the Lee-Carter and ARIMA models as it includes common stochastic long-run trends.
| Author | : Matteo Dimai |
| Publisher | : |
| Total Pages | : 0 |
| Release | : 2023 |
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Traditional stochastic mortality models tend to extrapolate, to focus on identifying trends in mortality without explaining them. Those that do link mortality with other variables usually limit themselves to GDP. This article presents a novel stochastic mortality model that incorporates a wide range of variables related to economic, environmental, and lifestyle factors to predict mortality. The model uses principal components derived from these variables in an extension of the Niu and Melenberg (2014) model and is applied to 37 countries from the Human Mortality Database. Model fit is superior to the Lee-Carter model for 18 countries. The forecasting accuracy of the proposed model is better than that of the Niu-Melenberg model for half of the countries analyzed under various jump-off years. The model is designed to facilitate scenario building and policy planning, providing insights into the interplay between different factors that affect mortality.
| Author | : Federico Girosi |
| Publisher | : Princeton University Press |
| Total Pages | : 294 |
| Release | : 2008-08-24 |
| Genre | : Social Science |
| ISBN | : 9780691130958 |
Demographic Forecasting introduces new statistical tools that can greatly improve forecasts of population death rates. Mortality forecasting is used in a wide variety of academic fields, and for policymaking in global health, social security and retirement planning, and other areas. Federico Girosi and Gary King provide an innovative framework for forecasting age-sex-country-cause-specific variables that makes it possible to incorporate more information than standard approaches. These new methods more generally make it possible to include different explanatory variables in a time-series regression for each cross section while still borrowing strength from one regression to improve the estimation of all. The authors show that many existing Bayesian models with explanatory variables use prior densities that incorrectly formalize prior knowledge, and they show how to avoid these problems. They also explain how to incorporate a great deal of demographic knowledge into models with many fewer adjustable parameters than classic Bayesian approaches, and develop models with Bayesian priors in the presence of partial prior ignorance. By showing how to include more information in statistical models, Demographic Forecasting carries broad statistical implications for social scientists, statisticians, demographers, public-health experts, policymakers, and industry analysts. Introduces methods to improve forecasts of mortality rates and similar variables Provides innovative tools for more effective statistical modeling Makes available free open-source software and replication data Includes full-color graphics, a complete glossary of symbols, a self-contained math refresher, and more
| Author | : Severine Arnold (-Gaille) |
| Publisher | : |
| Total Pages | : 0 |
| Release | : 2015 |
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| ISBN | : |
Modelling mortality and longevity risk is critical to assessing risk for insurers issuing longevity risk products. It has challenged practitioners and academics alike because of first the existence of common stochastic trends and second the unpredictability of an eventual mortality improvement in some age groups. When considering cause-of-death mortality rates, both aforementioned trends are additionally affected by the cause of death. Longevity trends are usually forecasted using a Lee-Carter model with a single stochastic time series for period improvements, or using an age-based parametric model with univariate time series for the parameters. We assess a multivariate time series model for the parameters of the Heligman-Pollard function, through Vector Error Correction Models which include the common stochastic long-run trends. The model is applied to circulatory disease deaths in U.S. over a 50-year period and is shown to be an improvement over both the Lee-Carter model and the stochastic parameter ARIMA Heligman-Pollard model.
| Author | : Shuo-Li Chuang |
| Publisher | : |
| Total Pages | : 316 |
| Release | : 2013 |
| Genre | : |
| ISBN | : |
The Lee-Carter mortality model provides the very first model for modeling the mortality rate with stochastic time and age mortality dynamics. The model is constructed modeling the mortality rate to incorporate both an age effect and a period effect. The Lee-Carter model provides the fundamental set up currently used in most modern mortality modeling. Various extensions of the Lee-Carter model include either adding an extra term for a cohort effect or imposing a stochastic process for mortality dynamics. Although both of these extensions can provide good estimation results for the mortality rate, applying them for the pricing of the mortality/ longevity linked derivatives is not easy. While the current stochastic mortality models are too complicated to be explained and to be implemented, transforming the cohort effect into a stochastic process for the pricing purpose is very difficult. Furthermore, the cohort effect itself sometimes may not be significant. We propose using a new modified Lee-Carter model with a Normal Inverse Gaussian (NIG) Lévy process along with the Esscher transform for the pricing of mortality/ longevity linked derivatives. The modified Lee-Carter model, which applies the Lee-Carter model on the growth rate of mortality rates rather than the level of iv mortality rates themselves, performs better than the current mortality rate models shown in Mitchell et al (2013). We show that the modified Lee-Carter model also retains a similar stochastic structure to the Lee-Carter model, so it is easy to demonstrate the implication of the model. We proposed the additional NIG Lévy process with Esscher transform assumption that can improve the fit and prediction results by adapting the mortality improvement rate. The resulting mortality rate matches the observed pattern that the mortality rate has been improving due to the advancing development of technology and improvements in the medical care system. The resulting mortality rate is also developed under a martingale measure so it is ready for the direct application of pricing the mortality/longevity linked derivatives, such as q-forward, longevity bond, and mortality catastrophe bond. We also apply our proposed model along with an information theoretic optimization method to construct the pricing procedures for a life settlement. While our proposed model can improve the mortality rate estimation, the application of information theory allows us to incorporate the private health information of a specific policy holder and hence customize the distribution of the death year distribution for the policy holder so as to price the life settlement. The resulting risk premium is close to the practical understanding in the life settlement market.
| Author | : Geng Niu |
| Publisher | : |
| Total Pages | : 0 |
| Release | : 2014 |
| Genre | : |
| ISBN | : |
The vast literature on extrapolative stochastic mortality models mainly focuses on the extrapolation of past mortality trends and summarizes the trends by one or more latent factors. However, the interpretation of these trends is typically not very clear. On the other hand, explanation methods are trying to link mortality dynamics with observable factors. This paper serves as an intermediate step between the two methods. We have performed a comprehensive analysis on the relationship between the latent trend in mortality dynamics and the trend in economic growth represented by GDP. Subsequently, the Lee-Carter framework is extended through the introduction of GDP as an additional factor next to the latent factor, which provides a better fit and better interpretable forecasts.
| Author | : Enrico Biffis |
| Publisher | : |
| Total Pages | : 19 |
| Release | : 2008 |
| Genre | : |
| ISBN | : |
We consider a class of stochastic intensities of mortality that generalizes the model proposed by Lee and Carter (1992), allowing general diffusions to drive the mortality time-trend. We analyze the stability of such class of intensities under measure changes and show how a risk-neutral version of the generalized Lee-Carter model can be employed for fair valuation purposes. We provide an example of model calibration based on the Italian annuity market.
| Author | : Meng Yu |
| Publisher | : |
| Total Pages | : 0 |
| Release | : 2013 |
| Genre | : Mortality |
| ISBN | : |
In this project, two approaches based on the linear logarithm hazard transform (LLHT) to modeling mortality rates are proposed. Empirical observations show that there is a linear relationship between two sequences of logarithm of the forces of mortality (hazard rates of the future lifetime) for two years. The estimated two parameters of the linear relationship can be used for forecasting mortality rates. Deterministic and stochastic mortality rates with the LLHT, Lee-Carter and CBD models are predicted, and their corresponding forecasted errors are calculated for comparing the forecasting performances. Finally, applications to pricing some mortality-linked securities based on the forecasted mortality rates are presented for illustration.
| Author | : Tommy Bengtsson |
| Publisher | : Springer |
| Total Pages | : 349 |
| Release | : 2019-03-28 |
| Genre | : Social Science |
| ISBN | : 3030050750 |
This open access book describes methods of mortality forecasting and discusses possible improvements. It contains a selection of previously unpublished and published papers, which together provide a state-of-the-art overview of statistical approaches as well as behavioural and biological perspectives. The different parts of the book provide discussions of current practice, probabilistic forecasting, the linearity in the increase of life expectancy, causes of death, and the role of cohort factors. The key question in the book is whether it is possible to project future mortality accurately, and if so, what is the best approach. This makes the book a valuable read to demographers, pension planners, actuaries, and all those interested and/or working in modelling and forecasting mortality.
