Stochastic mortality in a complex world: methodologies and applications within the affine diffusion framework

In this Thesis, we address the modelling of stochastic mortality, a key issue for life insurance, pension funds, public policy and fiscal planning. Indeed, the prospective increase of longevity can be an advantage for individuals, but it represents also a relevant social achievement. The stability and consistency of social welfare systems are put in danger worldwide due to the combined phenomenon of the progressive increase in life expectancy, along with the reduction of birth-rates in industrialized Countries. This phenomenon needs to be interpreted in the context of the connected world in which we live, where the multiple networks arising from the globalization, the Internet communication and the global economic development propagate any event in a very short time, making risks more complex. Due to their very nature, insurance and reinsurance deal with several risks on their balance sheet and, when determining the total risk of a portfolio, they need to establish the rules for aggregating the various risks that compose it. The introduction of market-consistent accounting and risk-based solvency requirements has called for the integration of mortality risk analysis into stochastic valuation models; moreover mortality-linked securities have attracted the interest of capital market investors, who in turn demand transparent tools to price demographic and financial risks in an integrated fashion. Accordingly, a coherent mathematical framework for studying the changes in financial and demographic conditions over time, is suitable. The class of the affine processes has been used in a wide range of applications in financial and actuarial sciences, thanks to its computational tractability and flexibility. For instance, affine processes have been extensively used in modelling the term structure of interest rates, that underpin extensive literatures on the pricing of bonds and interest-rate derivatives and are also at the basis of many of the pricing systems used by the financial industry. Affine models for the force of mortality have been developed in the literature under the assumption of both dependence and independence between mortality and interest rate dynamics. The core of this Thesis are the affine models and their properties for modelling the evolution of mortality. We propose and discuss two contributions: (i) we fit and compare past mortality trends among different Countries under the mathematical framework of the Feller process; (ii) we design a multiplicative affine model for the future evolution of mortality, by combining two components: the forecast provided by any existing mortality model, representing the deterministic baseline, and an affine driving process that stochastically affects the baseline over the forecasting time horizon. The so structured model not only is affine, thus fitting well our targets, but, when assessing its forecasting performance, it proves to be parsimonious and to provide a more accurate forecast with respect to the baseline. Within such a model, the affine driving factor is tasked with describing the dynamics over time of a measure of the fitting error of the existing mortality model providing the baseline and it is stochastically described by a Cox-Ingersoll-Ross process. For our numerical application, we choose, as the existing mortality model giving the baseline, the Cairns-Blake-Dowd (or M5) model, that is combined with the CIR process describing the stochastic factor affecting the baseline in a multiplicative way. The resulting model is called mCBD. Using the Italian females mortality data, for fixed ages, and implementing the backtesting procedure, over both a static time horizon and fixed-length windows rolling one-year ahead through time, we empirically test the performance of the CBD and the mCBD models in forecasting death rates. On the basis of average measures of forecasting errors and information criteria, we demonstrate that the mCBD model is a parsimonious model providing better results in terms of predictive accuracy than the CBD model and showing a stronger potential to gain accuracy in the long-run when a rolling windows analysis (dynamic approach) is performed. To conclude, in the Thesis, we explore and test the properties and capabilities of some affine models in fitting and forecasting mortality data both by themselves and as dynamic driving processes multiplying a deterministic baseline. Combining models and mixing techniques prove to give satisfactory results and show a concrete potential to bring the research forward. Our future research is thus oriented to use approaches that combine Monte Carlo simulations and benefit from the synergy between different techniques

A General framework for modelling mortality to better estimate its relationship with interest rate risks

The need for having a good knowledge of the degree of dependence between various risks is fundamental for understanding their real impacts and consequences, since dependence reduces the possibility to diversify the risks. This paper expands in a more theoretical approach the methodology developed in for exploring the dependence between mortality and market risks in case of stress. In particular, we investigate, using the Feller process, the relationship between mortality and interest rate risks. These are the primary sources of risk for life (re)insurance companies. We apply the Feller process to both mortality and interest rate intensities. Our study cover both the short and the long-term interest rates (3m and 10y) as well as the mortality indices of ten developed countries and extending over the same time horizon. Specifically, this paper deals with the stochastic modelling of mortality. We calibrate two different specifications of the Feller process (a two-parameters Feller process and a three-parameters one) to the survival probabilities of the generation of males born in 1940 in ten developed countries. Looking simultaneously at different countries gives us the possibility to find regularities that go beyond one particular case and are general enough to gain more confidence in the results. The calibration provides in most of the cases a very good fit to the data extrapolated from the mortality tables. On the basis of the principle of parsimony, we choose the two-parameters Feller process, namely the hypothesis with the fewer assumptions. These results provide the basis to study the dynamics of both risks and their dependence

A General framework for modelling mortality to better estimate its relationship with interest rate risks

The need for having a good knowledge of the degree of dependence between various risks is fundamental for understanding their real impacts and consequences, since dependence reduces the possibility to diversify the risks. This paper expands in a more theoretical approach the methodology developed in for exploring the dependence between mortality and market risks in case of stress. In particular, we investigate, using the Feller process, the relationship between mortality and interest rate risks. These are the primary sources of risk for life (re)insurance companies. We apply the Feller process to both mortality and interest rate intensities. Our study cover both the short and the long-term interest rates (3m and 10y) as well as the mortality indices of ten developed countries and extending over the same time horizon. Specifically, this paper deals with the stochastic modelling of mortality. We calibrate two different specifications of the Feller process (a two-parameters Feller process and a three-parameters one) to the survival probabilities of the generation of males born in 1940 in ten developed countries. Looking simultaneously at different countries gives us the possibility to find regularities that go beyond one particular case and are general enough to gain more confidence in the results. The calibration provides in most of the cases a very good fit to the data extrapolated from the mortality tables. On the basis of the principle of parsimony, we choose the two-parameters Feller process, namely the hypothesis with the fewer assumptions. These results provide the basis to study the dynamics of both risks and their dependence

Ultrasound-assisted green solvent extraction of high-added value compounds from microalgae Nannochloropsis spp.

The aim of this work was to investigate ultrasound (US)-assisted green solvent extraction of valuable compounds from the microalgae Nannochloropsis spp. Individual green solvents (water, ethanol (EtOH), dimethyl sulfoxide (DMSO)) and binary mixture of solvents (water-DMSO and water-EtOH) were used for the extraction procedures. Maximum total phenolic compounds yield (Yp 0.33) was obtained after US pre-treatment (W = 400 W, 15 min), being almost 5-folds higher compared to that found for the untreated samples and aqueous extraction (Yp 0.06). The highest yield of total chlorophylls (Yc 0.043) was obtained after US (W = 400 W, 7.5 min), being more than 9-folds higher than those obtained for the untreated samples and aqueous extraction (Yc 0.004). The recovery efficiency decreased as DMSO > EtOH > H2O. The optimal conditions to recover phenolic compounds and chlorophylls from microalgae were obtained after US pre-treatment (400 W, 5 min), binary mixtures of solvents (water-DMSO and water-EtOH) at 25–30%, and microalgae concentration of 10%

Impact of sleep disorders on behavioral issues in preschoolers with autism spectrum disorder

BackgroundSleep disorders are one of the most common problems in children with Autism Spectrum Disorder (ASD). However, they often tend to be underdiagnosed and incorrectly treated in clinical practice. This study aims to identify sleep disorders in preschool children with ASD and to explore their relationship with the core symptoms of autism, the child's developmental and cognitive level as well as the psychiatric comorbidities. MethodsWe recruited 163 preschool children with a diagnosis of ASD. The Children's Sleep Habits Questionnaire (CSHQ) assessed sleep conditions. Multiple standardized tests were used to evaluate intellectual abilities, the presence of repetitive behaviors (through the Repetitive Behavior Scale-Revised), as well as the emotional-behavioral problems and the psychiatric comorbidities (through the Child Behavior Checklist -CBCL 1(1/2)-5). ResultsThe results showed that poor disorders had consistently higher scores in all areas assessed by the CSHQ and on the CBCL across all domains. The correlational analysis showed that severe sleep disorders were associated with higher scores in internalizing, externalizing, and total problems at the CBCL syndromic scales, and in all DSM-oriented CBCL subscales. Moreover, we found that the association between sleep disorders and restricted and repetitive behaviors (RRBs) is explained by the anxiety-related symptoms. ConclusionBased on these findings, the study recommends that screening for sleep problems followed by early intervention should constitute a routine part of clinical practice for children with ASD

Corrective factors for longevity projections in a dynamic context

In light of the fact that forecasting longevity by updating data, dynami- cally in time, holds per se the capacity to improve the longevity projection itself with respect to the real phenomenon’s behavior, our interest is focused on the analysis and, specifically, on the measurement of the improvement effect resulting from implementing the dynamic forecasting procedure other than the static one. Actually, the study presented in this paper leads to the detection of corrective factors, of simple use and interpretation, allowing to increase the predictive accu- racy of the static forecast. The proposed corrective methodology is particularly suitable in the context of actuarial issues, especially those sensitive to the impact of dynamic factors such as longevity. For this reason, the numerical applications are based on the Cairns-Blake-Dowd model and on the old ages

A Comprehensive Study of Mortality Dynamics in Ten Developed Countries Using the Feller Process

The world in which we live is stochastic. Risks are becoming more and more complex because of their interconnectedness and the faster time scale at which we need to react to them. In order to cope with more complex risks, risk management should combine a scientific approach with a wide vision of reality. In particular, the need for having a good grasp of the degree of dependence between various risks is becoming more and more relevant and has been emphasized also by the current solvency regulations. We take the life (re)insurance companies perspective and study the relationship between their primary sources of risk: mortality and interest rate risks. We explore this through the Feller process applied to both mortality indices and interest rates of 10 countries

Gender Attitudes Toward Longevity and Retirement Planning: Theory and Evidence

This paper fosters discussion about the gender pension gap. We propose a research framework in financial economics, centered on the role of gender in longevity risk perception. Our approach is essentially made by three steps, aiming at the: (i) identification of drivers of subjective longevity assessment (e.g., biases), (ii) the measurement of the economic significance of longevity (mis)-perception in relation to saving and investment behaviors, (iii) the design of strategies to help women understand the opportunities behind long-term planning for retirement

Improving the Forecast of Longevity by Combining Models

Mortality is a dynamic process whose future evolution over time poses important challenges for life insurance, pension funds, public policy, and fiscal planning. In this paper, we propose two contributions: (1) a new dynamic corrective methodology of the predictive accuracy of the existing mortality projection models, by modeling a measure of their fitting errors as a Cox-Ingersoll- Ross process and; (2) various out-of-sample validation methods. Besides the usual static method, we develop a dynamic one allow- ing us to catch the change in behavior of the underlying data. For our numerical application, we choose the Cairns-Blake-Dowd (or M5) model. Using the Italian and French females mortality data and implementing the backtesting procedure, we empirically test the ex-post forecasting performance of the CBD model both for itself (CBD) and corrected by the CIR process (mCBD). We focus on age 65, but we show results for a wide range of ages, also much younger, and for cohort data. On the basis of average measures of forecasting errors and information criteria, we show that the mCBD model is parsimonious and provides better results in terms of predictive accuracy than the CBD model itself