Application of Machine Learning to Mortality Modeling and Forecasting

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

Maximum Market Price of Longevity Risk under Solvency Regimes: The Case of Solvency II.

Longevity risk constitutes an important risk factor for life insurance companies, and it can be managed through longevity-linked securities. The market of longevity-linked securities is at present far from being complete and does not allow finding a unique pricing measure. We propose a method to estimate the maximum market price of longevity risk depending on the risk margin implicit within the calculation of the technical provisions as defined by Solvency II. The maximum price of longevity risk is determined for a survivor forward (S-forward), an agreement between two counterparties to exchange at maturity a fixed survival-dependent payment for a payment depending on the realized survival of a given cohort of individuals. The maximum prices determined for the S-forwards can be used to price other longevity-linked securities, such as q-forwards. The Cairns–Blake–Dowd model is used to represent the evolution of mortality over time that combined with the information on the risk margin, enables us to calculate upper limits for the risk-adjusted survival probabilities, the market price of longevity risk and the S-forward prices. Numerical results can be extended for the pricing of other longevity-linked securities

A deep learning integrated Lee-Carter model

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

COVID-19 crisis and resilience: challenges for the insurance sector

The main role of the insurance sector is the coverage of risks through pooling techniques. Against the payment of a premium, the insurance company compensates for unexpected losses, including catastrophic events and pandemics. However, differently from a catastrophic event, the COVID-19 pandemic has highlighted that the global impact on economic and financial activities is highly correlated. The insurance sector itself has been strongly affected both by the exponential growth of claims in the life and non-life sectors and by the negative impact on financial activities. Past experiences in pandemic risk management have been unsuccessful. This paper retraces the instruments issued following the past pandemics and tries to reflect on how the insurance sector can implement innovative solutions to support post-pandemic resilience

A random forest algorithm to improve the Lee–Carter mortality forecasting: impact on q-forward

Increased life expectancy in developed countries has led researchers to pay more attention to mortality projection to anticipate changes in mortality rates. Following the scheme proposed in Deprez et al. (Eur Actuar J 7(2):337–352, 2017) and extended by Levantesi and Pizzorusso (Risks 7(1):26, 2019), we propose a novel approach based on the combination of random forest and two-dimensional P-spline, allowing for accurate mortality forecasting. This approach firstly provides a diagnosis of the limits of the Lee–Carter mortality model through the application of the random forest estimator to the ratio between the observed deaths and their estimated values given by a certain model, while the two-dimensional P-spline are used to smooth and project the random forest estimator in the forecasting phase. Further considerations are devoted to assessing the demographic consistency of the results. The model accuracy is evaluated by an out-of-sample test. Finally, we analyze the impact of our model on the pricing of q-forward contracts. All the analyses have been carried out on several countries by using data from the Human Mortality Database and considering the Lee–Carter model

Preface: recent developments in financial modelling and risk management

In the last decade, a wide range of innovative financial instruments has taken by storm the financial markets. In 2015 for instance, the European Commission (EC) introduced the definition of “innovative financial instruments” as instruments that are complementary to grants or subsidies and as part of a move towards a smarter “funding mix”. Loans, equity and quasi-equity instrument and guarantees are considered as a particularly effective way to increase and enhance the impact of EU funding while compared to the traditional grant-based system (EC, 2015), therefore, they represent a way to further promote a more responsible, result-oriented use of European funds by the corporate world

Machine Learning and Financial Literacy: An Exploration of Factors Influencing Financial Knowledge in Italy

In recent years, machine learning techniques have assumed an increasingly central role in many areas of research, from computer science to medicine, including finance. In the current study, we applied it to financial literacy to test its accuracy, compared to a standard parametric model, in the estimation of the main determinants of financial knowledge. Using recent data on financial literacy and inclusion among Italian adults, we empirically tested how tree-based machine learning methods, such as decision trees, random, forest and gradient boosting techniques, can be a valuable complement to standard models (generalized linear models) for the identification of the groups in the population in most need of improving their financial knowledge

The Importance of Economic Variables on London Real Estate Market: A Random Forest Approach

This paper follows the recent literature on real estate price prediction and proposes to take advantage of machine learning techniques to better explain which variables are more important in describing the real estate market evolution. We apply the random forest algorithm on London real estate data and analyze the local variables that influence the interaction between housing demand, supply and price. The variables choice is based on an urban point of view, where the main force driving the market is the interaction between local factors like population growth, net migration, new buildings and net supply

Financial sustainability and automatic balance mechanisms for NDC pension systems with disability benefits

The need for Long term care (LTC) service continues to rise due to the increasing number of elderly in the world, which stresses the healthcare systems. As most of the LTC recipients are over age 65, several authors studied retirement products combining a lifetime annuity with a long-term care benefit (typical examples are Enhanced Pension and Life Care Annuity). The development of an integrated strategy may help to address the issue of the cost of care for pensioners affected by disability. In this paper, we contribute to the debate on the introduction of LTC benefits into a notional defined contribution (NDC) pension system by using a multivariate stochastic model to represent the future evolution of transition probabilities and economic variables, which allows investigation of the financial sustainability of the system in a stochastic environment. The presence of LTC adds new risk elements, such as the uncertainty related to disability rates and mortality rates of the disabled, which may jeopardize the financial equilibrium of the integrated system. To restore the system's equilibrium, we apply two types of automatic balance mechanisms (ABM), one based on the solvency ratio, and the other on the liquidity ratio. Both act on the indexation of pensions and the notional rate