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29 pages, 1079 KiB

Open AccessArticle

Premium Risk Net of Reinsurance: From Short-Term to Medium-Term Assessment

by Antonio Pallaria and Nino Savelli

Risks 2019, 7(3), 72; https://doi.org/10.3390/risks7030072 - 1 Jul 2019

Viewed by 5279

Solvency II requirements introduced new issues for actuarial risk management in non-life insurance, challenging the market to have a consciousness of its own risk profile, and also investigating the sensitivity of the solvency ratio depending on the insurance risks and technical results on [...] Read more.

Solvency II requirements introduced new issues for actuarial risk management in non-life insurance, challenging the market to have a consciousness of its own risk profile, and also investigating the sensitivity of the solvency ratio depending on the insurance risks and technical results on either a short-term and medium-term perspective. For this aim, in the present paper, a partial internal model for premium risk is developed for three multi-line non-life insurers, and the impact of some different business mixes is analyzed. Furthermore, the risk-mitigation and profitability impact of reinsurance in the premium risk model are introduced, and a global framework for a feasible application of this model consistent with a medium-term analysis is provided. Numerical results are also figured out with evidence of various effects for several portfolios and reinsurance arrangements, pointing out the main reasons for these differences. Full article

(This article belongs to the Special Issue New Perspectives in Actuarial Risk Management)

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21 pages, 3850 KiB

Open AccessArticle

Experience Prospective Life-Tables for the Algerian Retirees

by Farid Flici and Frédéric Planchet

Risks 2019, 7(2), 38; https://doi.org/10.3390/risks7020038 - 4 Apr 2019

Cited by 2 | Viewed by 4407

Abstract

The aim of this paper is to construct prospective life tables adapted to the experience of Algerian retirees. Mortality data of the retired population are only available for the ages from 50 to 95 years and older and for the period from 2004 [...] Read more.

The aim of this paper is to construct prospective life tables adapted to the experience of Algerian retirees. Mortality data of the retired population are only available for the ages from 50 to 95 years and older and for the period from 2004 to 2013. The use of the conventional prospective mortality models is not supposed to provide robust forecasts given data limitation in terms of either exposure to death risk or data length. To improve forecasting robustness, we use the global population mortality as an external reference. The adjustment of the experience mortality on the reference allows projecting the age-specific death rates calculated based on the experience of the retired population. We propose a generalized version of the Brass-type relational model incorporating a quadratic effect to perform the adjustment. Results show no significant difference for men, either retired or not, but reveal a gap of over three years in the remaining life expectancy at age 50 in favor of retired women compared to those of the global population. Full article

(This article belongs to the Special Issue New Perspectives in Actuarial Risk Management)

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25 pages, 1058 KiB

Open AccessArticle

Mortality Projections for Small Populations: An Application to the Maltese Elderly

by Massimiliano Menzietti, Maria Francesca Morabito and Manuela Stranges

Risks 2019, 7(2), 35; https://doi.org/10.3390/risks7020035 - 29 Mar 2019

Cited by 3 | Viewed by 4529

Abstract

In small populations, mortality rates are characterized by a great volatility, the datasets are often available for a few years and suffer from missing data. Therefore, standard mortality models may produce high uncertain and biologically improbable projections. In this paper, we deal with [...] Read more.

In small populations, mortality rates are characterized by a great volatility, the datasets are often available for a few years and suffer from missing data. Therefore, standard mortality models may produce high uncertain and biologically improbable projections. In this paper, we deal with the mortality projections of the Maltese population, a small country with less than 500,000 inhabitants, whose data on exposures and observed deaths suffers from all the typical problems of small populations. We concentrate our analysis on older adult mortality. Starting from some recent suggestions in the literature, we assume that the mortality of a small population can be modeled starting from the mortality of a bigger one (the reference population) adding a spread. The first part of the paper is dedicated to the choice of the reference population, then we test alternative mortality models. Finally, we verify the capacity of the proposed approach to reduce the volatility of the mortality projections. The results obtained show that the model is able to significantly reduce the uncertainty of projected mortality rates and to ensure their coherent and biologically reasonable evolution. Full article

(This article belongs to the Special Issue New Perspectives in Actuarial Risk Management)

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16 pages, 5864 KiB

Open AccessArticle

A Deep Learning Integrated Lee–Carter Model

by Andrea Nigri, Susanna Levantesi, Mario Marino, Salvatore Scognamiglio and Francesca Perla

Risks 2019, 7(1), 33; https://doi.org/10.3390/risks7010033 - 16 Mar 2019

Cited by 65 | Viewed by 11182

Abstract

In the field of mortality, the Lee–Carter based approach can be considered the milestone to forecast mortality rates among stochastic models. We could define a “Lee–Carter model family” that embraces all developments of this model, including its first formulation (1992) that remains the [...] Read more.

In the field of mortality, the Lee–Carter based approach can be considered the milestone to forecast mortality rates among stochastic models. We could define a “Lee–Carter model family” that embraces all developments of this model, including its first formulation (1992) that remains the benchmark for comparing the performance of future models. In the Lee–Carter model, the

κ_{t}

parameter, describing the mortality trend over time, plays an important role about the future mortality behavior. The traditional ARIMA process usually used to model

κ_{t}

shows evident limitations to describe the future mortality shape. Concerning forecasting phase, academics should approach a more plausible way in order to think a nonlinear shape of the projected mortality rates. Therefore, we propose an alternative approach the ARIMA processes based on a deep learning technique. More precisely, in order to catch the pattern of

κ_{t}

series over time more accurately, we apply a Recurrent Neural Network with a Long Short-Term Memory architecture and integrate the Lee–Carter model to improve its predictive capacity. The proposed approach provides significant performance in terms of predictive accuracy and also allow for avoiding the time-chunks’ a priori selection. Indeed, it is a common practice among academics to delete the time in which the noise is overflowing or the data quality is insufficient. The strength of the Long Short-Term Memory network lies in its ability to treat this noise and adequately reproduce it into the forecasted trend, due to its own architecture enabling to take into account significant long-term patterns. Full article

(This article belongs to the Special Issue New Perspectives in Actuarial Risk Management)

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19 pages, 2219 KiB

Open AccessArticle

Application of Machine Learning to Mortality Modeling and Forecasting

by Susanna Levantesi and Virginia Pizzorusso

Risks 2019, 7(1), 26; https://doi.org/10.3390/risks7010026 - 26 Feb 2019

Cited by 41 | Viewed by 10799

Abstract

Estimation of future mortality rates still plays a central role among life insurers in pricing their products and managing longevity risk. In the literature on mortality modeling, a wide number of stochastic models have been proposed, most of them forecasting future mortality rates [...] Read more.

Estimation of future mortality rates still plays a central role among life insurers in pricing their products and managing longevity risk. In the literature on mortality modeling, a wide number of stochastic models have been proposed, most of them forecasting future mortality rates by extrapolating one or more latent factors. The abundance of proposed models shows that forecasting future mortality from historical trends is non-trivial. Following the idea proposed in Deprez et al. (2017), we use machine learning algorithms, able to catch patterns that are not commonly identifiable, to calibrate a parameter (the machine learning estimator), improving the goodness of fit of standard stochastic mortality models. The machine learning estimator is then forecasted according to the Lee-Carter framework, allowing one to obtain a higher forecasting quality of the standard stochastic models. Out-of sample forecasts are provided to verify the model accuracy. Full article

(This article belongs to the Special Issue New Perspectives in Actuarial Risk Management)

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13 pages, 3615 KiB

Open AccessArticle

An Indexation Mechanism for Retirement Age: Analysis of the Gender Gap

by Mariarosaria Coppola, Maria Russolillo and Rosaria Simone

Risks 2019, 7(1), 21; https://doi.org/10.3390/risks7010021 - 22 Feb 2019

Cited by 7 | Viewed by 3671

Abstract

The management of National Social Security Systems is being challenged more and more by the rapid ageing of the population, especially in the industrialized countries. In order to chase the Pension System sustainability, several countries in Europe are setting up pension reforms linking [...] Read more.

The management of National Social Security Systems is being challenged more and more by the rapid ageing of the population, especially in the industrialized countries. In order to chase the Pension System sustainability, several countries in Europe are setting up pension reforms linking the retirement age and/or benefits to life expectancy. In this context, the accurate modelling and projection of mortality rates and life expectancy play a central role and represent issues of great interest in recent literature. Our study refers to the Italian mortality experience and considers an indexing mechanism based on the expected residual life to adjust the retirement age and keep costs at an expected budgeted level, in the spirit of sharing the longevity risk between Social Security Systems and retirees. In order to combine fitting and projections performances of selected stochastic mortality models, a model assembling technique is applied to face uncertainty in model selection, while accounting for uncertainty of estimation as well. The resulting proposal is an averaged model that is suitable to discuss about the gender gap in longevity risk and its alleged narrowing over time. Full article

(This article belongs to the Special Issue New Perspectives in Actuarial Risk Management)

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27 pages, 6327 KiB

Open AccessArticle

Can Pension Funds Partially Manage Longevity Risk by Investing in a Longevity Megafund?

by Edouard Debonneuil, Anne Eyraud-Loisel and Frédéric Planchet

Risks 2018, 6(3), 67; https://doi.org/10.3390/risks6030067 - 2 Jul 2018

Cited by 2 | Viewed by 6272

Abstract

Pension funds, which manage the financing of a large share of global retirement schemes, need to invest their assets in a diversified manner and over long durations while managing interest rate and longevity risks. In recent years, a new type of investment has [...] Read more.

Pension funds, which manage the financing of a large share of global retirement schemes, need to invest their assets in a diversified manner and over long durations while managing interest rate and longevity risks. In recent years, a new type of investment has emerged, that we call a longevity megafund, which invests in clinical trials for solutions against lifespan-limiting diseases and provides returns positively correlated with longevity. After describing ongoing biomedical developments against ageing-related diseases, we model the needed capital for pension funds to face longevity risk and find that it is far above current practices. After investigating the financial returns of pharmaceutical developments, we estimate the returns of a longevity megafund. Combined, our models indicate that investing in a longevity megafund is an appropriate method to significantly reduce longevity risk and the associated economic capital need. Full article

(This article belongs to the Special Issue New Perspectives in Actuarial Risk Management)

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19 pages, 930 KiB

Open AccessArticle

Risk Aversion, Loss Aversion, and the Demand for Insurance

by Louis Eeckhoudt, Anna Maria Fiori and Emanuela Rosazza Gianin

Risks 2018, 6(2), 60; https://doi.org/10.3390/risks6020060 - 25 May 2018

Cited by 12 | Viewed by 7038

Abstract

In this paper we analyze insurance demand when the utility function depends both upon final wealth and the level of losses or gains relative to a reference point. Besides some comparative statics results, we discuss the links with first-order risk aversion, with the [...] Read more.

In this paper we analyze insurance demand when the utility function depends both upon final wealth and the level of losses or gains relative to a reference point. Besides some comparative statics results, we discuss the links with first-order risk aversion, with the Omega measure, and with a tendency to over-insure modest risks that has been been extensively documented in real insurance markets. Full article

(This article belongs to the Special Issue New Perspectives in Actuarial Risk Management)

18 pages, 373 KiB

Open AccessArticle

On Two Mixture-Based Clustering Approaches Used in Modeling an Insurance Portfolio

by Tatjana Miljkovic and Daniel Fernández

Risks 2018, 6(2), 57; https://doi.org/10.3390/risks6020057 - 17 May 2018

Cited by 10 | Viewed by 4226

Abstract

We review two complementary mixture-based clustering approaches for modeling unobserved heterogeneity in an insurance portfolio: the generalized linear mixed cluster-weighted model (CWM) and mixture-based clustering for an ordered stereotype model (OSM). The latter is for modeling of ordinal variables, and the former is [...] Read more.

We review two complementary mixture-based clustering approaches for modeling unobserved heterogeneity in an insurance portfolio: the generalized linear mixed cluster-weighted model (CWM) and mixture-based clustering for an ordered stereotype model (OSM). The latter is for modeling of ordinal variables, and the former is for modeling losses as a function of mixed-type of covariates. The article extends the idea of mixture modeling to a multivariate classification for the purpose of testing unobserved heterogeneity in an insurance portfolio. The application of both methods is illustrated on a well-known French automobile portfolio, in which the model fitting is performed using the expectation-maximization (EM) algorithm. Our findings show that these mixture-based clustering methods can be used to further test unobserved heterogeneity in an insurance portfolio and as such may be considered in insurance pricing, underwriting, and risk management. Full article

(This article belongs to the Special Issue New Perspectives in Actuarial Risk Management)

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