An Efficient Method for Mitigating Longevity Value-at-Risk

This study sets out a backtesting framework applicable to the multiperiod-ahead forecasts from stochastic mortality models and uses it to evaluate the forecasting performance of six different stochastic mortality models applied to English & Welsh male mortality data. The models considered are the following: Lee-Carter’s 1992 one-factor model; a version of Renshaw-Haberman’s 2006 extension of the Lee-Carter model to allow for a cohort effect; the age-period-cohort model, which is a simplified version of Renshaw-Haberman; Cairns, Blake, and Dowd’s 2006 two-factor model; and two generalized versions of the last named with an added cohort effect. For the data set used herein, the results from applying this methodology suggest that the models perform adequately by most backtests and that prediction intervals that incorporate parameter uncertainty are wider than those that do not. We also find little difference between the performances of five of the models, but the remaining model shows considerable forecast instability.

Proposed by Chan, Li, and Li, parametric mortality indexes (i.e., indexes created using the time-varying parameters in a suitable stochastic mortality model) can be used to develop tradable mortality-linked derivatives such as K-forwards. Compared to existing indexes such as the Life and Longevity Markets Association’s LifeMetrics, parametric mortality indexes are richer in information content, allowing the market to better concentrate liquidity. In this article, we further study this concept in several aspects. First, we consider options written on parametric mortality indexes. Such options enable hedgers to create out-of-the-money longevity hedges, which, compared to at-the-money-hedges created with q-/K-forwards, may better meet hedgers’ needs for protection against downside risk. Second, using the properties of the time series processes for the parametric mortality indexes, we derive analytical risk-neutral pricing formulas for K-forwards and options. In addition to convenience, the analytical pricing formulas remove the need for computationally intensive nested simulations that are entailed in, for example, the calculation of the hedging instruments’ values when a dynamic hedge is adjusted. Finally, we construct static and dynamic Greek hedging strategies using K-forwards and options, and demonstrate empirically the conditions under which an out-of-the-money hedge is more economically justifiable than an at-the-money one.

Bir fabrikanın üretim sürecinin kalitesini kontrol etmek amacıyla kullandığı en hızlı, ve güvenilir yöntemlerden biri klasik Shewhart kontrol kartlarıdır. Ancak küçük örneklem durumunda, normal dağılım varsayımının şüpheli olduğu durumlarda ve çarpık ya da ağır kuyruklu dağılım söz konusu olduğunda Shewhart kontrol kartı ile süreci takip etmek riskli olacaktır. Böyle durumlarda parametrik olmayan kontrol kartları tercih edilir. Bu çalışmada tek taraflı parametrik olmayan kontrol kartları ayrıntılı olarak incelenmiştir. Ön istatistiğe dayalı tek taraflı medyan kontrol kartı için yanlış alarm oranı, çalışma uzunluğu ve ortalama çalışma uzunluğunun değerleri hesaplanmıştır. Medyan kontrol kartlarının tek dezavantajı hesaplamalarının güçlüğüdür. Bu güçlüğü gidermek için farklı örneklem hacimleri ve farklı olasılıklar için yapılan hesaplamalar orijinal tablolarda sunulmuştur. Ülkemizde üretim yapan ve istatistiksel kalite kontrol sürecine önem veren sanayi kuruluşları için hazırlanan bu tablolar büyük kolaylıklar sağlayacaktır. Çalışmanın sonunda bir veri seti üzerinde uygulama yapılarak ön istatistiğine dayalı medyan kontrol kartının kullanımı gösterilmiştir.

In this paper we mirror the framework of generalized (non-)linear models to define the family of generalized age-period-cohort stochastic mortality models which encompasses the vast majority of stochastic mortality projection models proposed to date, including the well-known Lee-Carter and Cairns-Blake-Dowd models. We also introduce the R package StMoMo which exploits the unifying framework of the generalized age-period-cohort family to provide tools for fitting stochastic mortality models, assessing their goodness of fit and performing mortality projections. We illustrate some of the capabilities of the package by performing a comparison of several stochastic mortality models applied to the England and Wales population.

PurposeThis paper aims to assess all the Brazilian electric power transmission line auctions occurred between 1999 and 2017.Design/methodology/approachA copula-based Roy/endogenous switching regression model is used. The suitability of this model is twofold: it takes into account the selection bias problem involving auctions data and it allows more flexibility in modeling the joint distribution between the unobserved components of the selection and outcome equations; thus, normal distribution assumptions are not needed.FindingsThe main results suggest that stated-owned companies have the highest probability of winning an auction, and there is a non-competitive behavior among the players in the auction. The results also suggest some departure from joint normality in the data.Originality/valueThe copula-based sample selection approach used in this paper is consistent under non-normality and allows one to address different types of nonlinearities in the data such as asymmetry and heavy tails.

In this paper, we address the mortality modeling needs for pension plan sponsors who wish to use index-based solutions to mitigate their longevity risk exposures. Specifically, we propose the three-way Li-Lee (TWLL) model, which enforces a certain extent of coherence between the population to which the index-based hedging instrument is linked and the population of pension plan members, and at the same time incorporates the empirical fact that mortality improvement rates of different socioeconomic subgroups in the pension plan are persistently different. We further develop a delta longevity hedging strategy that is compatible with the TWLL model. With the aid of real mortality data, we demonstrate that if persistent socioeconomic differentials in mortality improvement rates exist but are not considered in an index-based longevity hedge, the performance of the hedge could be compromised, and the extent of underperformance would depend on the distributions of pension plan members and pension amounts across different socioeconomic subgroups. This problem can be alleviated if the longevity hedge is calibrated on the basis of the TWLL model.

BackgroundPrecise predictions of incidence and mortality rates due to breast cancer (BC) are required for planning of public health programs as well as for clinical services. A number of approaches has been established for prediction of mortality using stochastic models. The performance of these models intensely depends on different patterns shown by mortality data in different countries.MethodsThe BC mortality data is retrieved from the Global burden of disease (GBD) study 2017 database. This study include BC mortality rates from 1990 to 2017, with ages 20 to 80+ years old women, for different Asian countries. Our study extend the current literature on Asian BC mortality data, on both the number of considered stochastic mortality models and their rigorous evaluation using multivariate Diebold-Marino test and by range of graphical analysis for multiple countries.ResultsStudy findings reveal that stochastic smoothed mortality models based on functional data analysis generally outperform on quadratic structure of BC mortality rates than the other lee-carter models, both in term of goodness of fit and on forecast accuracy. Besides, smoothed lee carter (SLC) model outperform the functional demographic model (FDM) in case of symmetric structure of BC mortality rates, and provides almost comparable results to FDM in within and outside data forecast accuracy for heterogeneous set of BC mortality rates.ConclusionConsidering the SLC model in comparison to the other can be obliging to forecast BC mortality and life expectancy at birth, since it provides even better results in some cases. In the current situation, we can assume that there is no single model, which can truly outperform all the others on every population. Therefore, we also suggest generating BC mortality forecasts using multiple models rather than relying upon any single model.

Basically, all stock investments aim to obtain maximum profit with low risk. The formation of a stock investment portfolio is always accompanied by measuring returns and risks that show its performance. Portfolio risk measurement is often faced with the challenge that returns are not normally distributed, so that measurements using the normality assumption cannot be applied. This study proposes the development of a modification of stock portfolio risk measurement so that it is not limited to the normality assumption. The development is carried out by modifying the calculation of Value at Risk (VaR) to consider the skewness and kurtosis values ​​(hereinafter referred to as modified VaR), so that the normal distribution assumption can be eliminated. As a method for compiling a stock portfolio, the Multi-Objective Optimization technique was chosen because it can modify risk averse so that the risk can be adjusted to the risk profile of each investor and is able to stabilize the mean return value. For its implementation, this paper uses real stock data which of course has returns that are not normally distributed, namely the four Indonesian stocks based on the largest capitalization recorded in January 2025 (blue chip), namely BREN, BBCA, BYAN, and BBRI obtained through finance.yahoo.com. The analysis method is divided into three steps, including multi-objective optimization completion, portfolio return calculation, and finally modified VaR estimation. The results of the study show that BBCA has the largest weight with a portion of more than 40% of the four stocks, so BBCA will be the priority stock for this portfolio. The portfolio formed using multi-objective optimization is proven to have a stable mean return because the portfolio mean return is between several of its constituent stocks (vice versa) which is around 0.01%, and the smallest estimated value of the portfolio modified VaR is 1.67%. Thus, a portfolio based on multi-objective optimization is not only able to create a portfolio that provides a small risk in risk measurement without assuming a normal distribution, but at the same time multi-objective optimization is also able to provide competitive returns with its constituent stocks.

Human lifespan increments represent one of the main current risks for governments and pension and health benefits providers. Longevity societies imply financial sustainability challenges to guarantee adequate socioeconomic conditions for all individuals for a longer period. Consequently, modelling population dynamics and projecting future longevity scenarios are vital tasks for policymakers. As an answer, the demographic and the actuarial literature have been introduced and compared to several stochastic mortality models, although few studies have thoroughly tested the uncertainty concerning mortality projections. Forecasting mortality uncertainty levels have a central role since they reveal the potential, unexpected longevity rise and the related economic impact. Therefore, the present study poses a methodological framework to backtest uncertainty in mortality projections by exploiting uncertainty metrics not yet adopted in mortality literature. Using the data from the Human Mortality Database of the male and female populations of five countries, we present some numerical applications to illustrate how the proposed criterion works. The results show that there is no mortality model overperforming the others in all cases, and the best model choice depends on the data considered.

Mortality Density Forecasts: An Analysis of Six Stochastic Mortality Models

This study aims to investigate the impact of China’s new fertility policy on the actuarial balance of its Urban Employee Basic Endowment Insurance (UEBEI) fund, with stochastic mortality model included to address the longevity risk. Combined with the latest UEBEI policy, this paper constructs an actuarial balance model and introduces the growth rate of wage, the age of employment and the age of retirement, the rate of payment, the rate of replacement, the annual rate of pension adjustment, and the population in terms of age into the model, which arise from the rate of payment, average wage, and personal and social factors. This study uses the sixth population census data by age group and gender to employ empirical analysis. The sensitivity analysis of China’s basic pension insurance fund balance is made. It is concluded that the increase in the growth rate of wage caused by social factors, the increase of fund investment returns, the delay of retirement, and the increase in the fund collection rate are all conducive to the sustainability of the UEBEI fund.

For the life insurance industry and pension schemes, mortality projections are critical for accurately managing exposure to longevity risk in terms of both premium setting and reserving. Frailty has been identified as an important latent factor underpinning the evolution of mortality rates. It represents the comorbidities that drive the deterioration of the human body’s physiological capacity. In this paper, we propose a stochastic mortality model that incorporates the trend in frailty, and we analyse the gap between the actuarial evaluations of premiums and technical provisions calculated under frailty-based and traditional stochastic mortality models. We observe that the frailty-based model leads to higher levels of uncertainty in estimates and projections (compared to a traditional stochastic mortality model), which is attributed to the explicit modelling of the comorbidities. This leads to proposing a potentially important policy-oriented recommendation: the incorporation of frailty in mortality modelling would allow for the profiling of mortality according to the portfolio in force for the insurer (or pension scheme), thereby mitigating the problem of adverse selection.

In this paper, we propose a fractional stochastic volatility jump-diffusion model which extends the Bates(1996) model. Where we model the volatility as a fractional process. Extensive empirical studies show that the distributions of the logarithmic returns of financial asset usually exhibit properties of self-similarity and long-range dependence and since the fractional Brownian motion has these two important properties, it has the ability to capture the behavior of underlying asset price. Further incorporating jumps into the stochastic volatility framework gives further freedom to financial mathematicians to fit both the short and long end of the implied volatility surface. We propose a stochastic model which contains both fractional and jump process. Then we price options using Monte Carlo simulations along with a variance reduction technique(antithetic variates). We use market data from the S&P 500 index and we compare our results with the Heston and Bates model using error measures. The results show our model greatly outperforms previous models in terms of estimation accuracy.

The insurance enterprise faces growing challenges in optimizing annuity pricing strategies under changing market situations and growing opposition to its product portfolios. Conventional actuarial models have massive deficiencies, as they depend upon historical data patterns and linear assumptions that cannot capture complex, nonlinear relationships among risk factors and profitability results. The usage of machine learning algorithms in annuity pricing frameworks truly addresses core shortcomings in conventional methodologies, with particular regard to mortality risk assessment, sensitivity analysis of interest rates, and policyholder behavior prediction. Gradient boosting decision trees, neural network architectures, and ensemble methods applied to fixed and indexed annuity products achieve superior predictive accuracy compared to generalized linear models commonly found in traditional actuarial practice. This implementation framework integrates machine learning predictive capabilities with established actuarial practices to ensure regulatory compliance while maintaining mathematical soundness. Deep learning approaches to mortality forecasting, especially Long Short-Term Memory networks, transcend restrictions of classical Lee-Carter models by allowing temporal dependencies and nonlinear patterns to be captured, characteristic of modern mortality experiences. Reinforcement learning applications to derivative hedging strategies optimize dynamic rebalancing decisions for indexed annuity products with embedded options. Quantitative comparison among stochastic mortality models across heterogeneous populations reveals performance differences conditional upon demographic characteristics and projection horizons. Spread margin enhancement through predictive analytics allows a more sophisticated crediting rate determination and policyholder retention strategy. ROI considerations include not only direct improvements in profitability but also indirect operational efficiency gains, balanced against infrastructure and personnel investment requirements.

Systematic Mortality Risk: An Analysis of Guaranteed Lifetime Withdrawal Benefits in Variable Annuities