New Perspectives in Mathematical and Statistical Methods for Actuarial Sciences and Finance

Table of Contents

1. Frontmatter

2. Towards Fairer Sanction Systems: Income-Based Models with Aggregation Functions

   Luca Anzilli, Marta Cardin, Silvio Giove

   Abstract

   This paper presents a novel framework for designing income-based fines that integrate both the severity of the offence and the financial capacity of the offender. The model employs a grid-based interpolation approach, initially using bilinear interpolation and then extending to more expressive aggregation techniques such as the Choquet integral and t-norms. This generalization allows for customizable sanction functions that reflect diverse legal and ethical priorities. Numerical simulations illustrate the impact of different aggregation strategies on fine outcomes.

3. Multidimensional Inequality and Measurement of Social Well-Being

   Luca Anzilli, Marta Cardin, Silvio Giove

   Abstract

   In recent times, multidimensional measures of well-being are being utilized more widely within academic research and policy assessments. Understanding the multidimensional aspects of well-being is crucial for accurate measurement. This paper explores different types of societal well-being measures through an axiomatic framework while addressing the issue of inequality aversion. Different approaches to measuring inequality in a multidimensional framework are discussed.

4. A Neural Network Model Approach to Longevity Risk Management

   Giovanna Apicella, Michele La Rocca, Cira Perna, Marilena Sibillo

   Abstract

   Insurance activities intrinsically deal with the management of risks. According to the mark-to-model approach to the assessment of the insurer’s debt position, the models used to forecast the probability structures involved in the computation of the fair value of the liabilities are central. We use artificial neural networks to the purpose of forecasting in this context. We focus on a portfolio of endowment insurance policies and on the ex ante estimation of the related mathematical reserve. We consider the Lee-Carter model for the forecasting of the random number of the policies in-force at each future policy anniversary, with either linear time-series model or autoregressive neural network models (ARX-NN models)for the time index. We find out that ARX-NN models allow to reduce the bias that linear time series models may imply. In particular, narrower prediction intervals around central forecasts translates into a much milder upward shift of the portfolio reserve in the case where systematic reduced mortality than expected should occur along the insurance contracts’ duration.

5. Climate-Related Extensions of the Lee-Carter Model

   Imma Lory Aprea, Francesca Perla, Raffaele Clemente Petrella, Mariafortuna Pietroluongo, Salvatore Scognamiglio

   Abstract

   This study examines the impact of climate risk-related variables on mortality patterns across diverse population groups. An innovative version of the Lee-Carter model is proposed, incorporating a climate risk-related variable - specifically, \(\text {CO2}\) emissions - to enhance the accuracy of mortality prediction. A three-step estimation process using Ordinary Least Squares is employed to calibrate the model parameters. Experiments conducted on data from 42 populations indicate that integrating climate risk information leads to more accurate mortality predictions. Especially, combining climate variables with macroeconomic indicators such as GDP yields further improvements in forecast performance.

6. Quantification of Operational Flexibility in Wastewater Treatment Projects

   Marta Biancardi, Antonio Di Bari, Giovanni Villani

   Abstract

   Today, wastewater treatment projects are very important to preserve human health and the terrestrial and aquatic ecosystems. The valuation of these projects presents some difficulties related to the uncertainty of wastewater flows over time and the operational flexibilities that influences their performance.

   This paper aims to provide a valuation methodology of wastewater treatment projects that can consider the stochastic nature of the wastewater volume, the operational flexibility to expand the project, and the possibility of turning off the system when the wastewater volume is too low to avoid financial losses. To pursue this goal, we apply a Real Options Approach (ROA) fitted for the characteristics of the wastewater volume in an agricultural firm, such as its evolution through a standard Brownian motion to which it is applied a seasonality component referred to the availability of fruits and vegetables in certain months. We also propose a case study related to a wastewater treatment project carried out by the Rosso Gargano Company in southern Italy.

7. Roughness in VIX Index and in Realized Volatility: Rolling Window Estimation by Randomized Kolmogorov-Smirnov Distribution

   Sergio Bianchi, Daniele Angelini

   Abstract

   The modeling and forecasting of financial market volatility constitute fundamental components of effective risk management and optimal asset allocation. Traditional models like GARCH and SV often fail to capture the long memory and roughness empirically observed in volatility, prompting the adoption of fractional processes. Accurate estimation of the log-volatility roughness parameter is thus key to validating rough volatility models, with several methodologies proposed, including spectral, wavelet, and machine learning techniques. In contrast to approaches focused on moment behavior, we adopt a novel method based on the self-similarity of fractional processes, examining how the entire log-volatility distribution scales across time horizons. We deduce the variance of the estimator and study the roughness of both CBOE VIX and realized volatility.

8. A Comparison of Data-Driven Synthetic Performance Indicators for Default Prediction

   Roberto Casarin, Fausto Corradin, Antonio Peruzzi

   Abstract

   This paper compares two approaches to constructing synthetic performance indicators for corporate default prediction: the expert-informed Synthetic Performance Indicator (ISP) and a Neural Network Synthetic Performance Indicator (NNISP). Both are built upon a common set of economic and financial indices from a large panel of firms operating in the Triveneto macro-region of Italy, including not only large companies but also small and medium enterprises (SMEs). The ISP relies on expert elicitation to assign weights to eight selected indicators, while the NNISP is obtained by calibrating the set of composition weights by training a Neural Network to predict a firm’s liquidity. We assess the predictive power of each score using multiple classification models and benchmark them against the full set of indicators. We show that the ISP offers stable and interpretable performance across model types, while the NNISP exhibits more flexibility in non-linear settings. These findings highlight a trade-off between expert-based interpretability and machine-driven adaptability, pointing to the potential of combined methodologies for future applications in credit risk modeling.

9. Rethinking the Indexation of Retirement Age: Cohort vs. Period Life Expectancy

   Mariarosaria Coppola, Maria Russolillo, Rosaria Simone

   Abstract

   Over the past two centuries, life expectancy has risen steadily in industrialized countries, challenging the financial sustainability of pension systems. In systems with indexed pension age, a key issue is whether to use period life expectancy (PLE) or cohort life expectancy (CLE). CLE relies on real cohort data and captures future mortality improvements; requiring a full lifespan of data, it can be estimated only for extinct cohorts. To address this, CLE is often estimated using life tables combining past and expected future mortality. In contrast, PLE is based on mortality rates observed in a single period. It is simpler but less accurate than CLE, particularly when assessing the retirement systems sustainability. The aim of this paper is twofold: measuring the gap between CLE and PLE at age 65 for Italian population using Lee-Carter and Renshaw-Haberman models for mortality projections, and assessing how this gap affects the pension age shift.

10. Calibrating Temperature Models with Neural Networks for Weather Derivatives

    Stefania Corsaro, Vincenzo Di Sauro, Zelda Marino, Salvatore Scognamiglio

    Abstract

    Weather significantly affects business activities, making hedging against related risks crucial; weather derivatives can help mitigate financial impacts. Most of the derivatives currently traded are linked to a temperature; having a good model for its evolution is the backbone of effective weather derivative pricing. This paper presents a novel neural network approach for jointly calibrating the mean and variance of temperature for weather derivatives pricing. We also address the challenge of explainability in neural networks by designing the architecture to replace the approach proposed in [1]. Additionally, we explore potential extensions of the model to improve forecasting accuracy further. Through numerical experiments with weather station data from Fiumicino Maccarese, we illustrate the model’s application in pricing Heating Degree Day futures.

11. Modeling Health and Disability Trajectories in Later Life: A Multi-state Approach Using HRS Data

    Domenico De Giovanni, Massimiliano Menzietti, Marco Pirra, Fabio Viviano

    Abstract

    This paper develops a continuous-time multi-state Markov model to analyze health and disability transitions in later life using data from the Health and Retirement Study (HRS). We define five distinct states combining health and functional status, allowing for 12 possible transitions including recovery and death. Transition intensities are estimated via a proportional hazards framework, incorporating individual-specific and time-dependent covariates. Model selection is guided by likelihood-based criteria, and results highlight significant heterogeneity by age, gender, and baseline condition. We derive one-year transition probabilities and compute dynamic life expectancies by initial state. Our findings reveal persistent disparities in ageing trajectories and underscore the importance of distinguishing between health and disability dimensions. The model offers practical insights for projecting future health burdens and designing long-term care strategies.

12. Backtesting Expected Shortfall for Bitcoin: A Joint Combined LSTM-Based Approach

    Giovanni De Luca, Anna Pia Di Iorio, Andrea Montanino

    Abstract

    This work aims to identify the most accurate model in passing the joint-combined backtesting procedure for Value-at-Risk and Expected Shortfall forecasts for Bitcoin. First, GARCH and Markov Switching GARCH are estimated and used to forecast the corresponding VaR and ES. Next, the Long Short-Term Memory model is applied to refine these risk measures. Finally, four models (GARCH, Markov-Switching GARCH, Joint-Combined, Long-Short Term Memory Joint-Combined) are compared based on average loss and backtesting performances. Results suggest that the LSTM-Joint-Combined model apparently represents the best model delivering the lowest average predictive loss across the evaluated settings. Furthermore, it considerably enhances the efficacy of the JC approach.

13. Understanding and Attitudes Toward Reverse Mortgage in Italy: Cognitive Dissonance and Future Concerns

    Emilia Di Lorenzo, Alba Roviello

    Abstract

    Reverse Mortgage (RM), known as Prestito Ipotecario Vitalizio (PIV) in Italy, is an alternative financing solution aimed at individuals aged 60 and above who typically lack access to conventional credit lines. Subscribing the RM allows elders homeowners to convert part of their home’s equity into a lump sum or periodic payments preserving the right to live in the house and, differently from the bare ownership, without losing any legal rights on the property. The loan, along with accumulated interest, has to be repaid only when the borrower dies, sells the home, or permanently moves out. The Non-Negative Equity Guarantee (NNEG) protects the heirs by ensuring that, if the property’s value at the time of loan repayment is insufficient to cover the outstanding debt, no additional amount is required. Despite its availability in the Italian market for several years, RM remains a relatively underutilized financial instrument. To assess current levels of awareness and identify the barriers limiting access to this property-linked financing option, we present some preliminary results obtained conducting a comprehensive qualitative and quantitative research study among potential Italian subscribers, which takes into account individuals’ future concern about economic sustainability, their understanding and knowledge of supplementary pension products with priority over RM and actual interest in or use of the product. The objective is to provide meaningful insights into Italian perception of the Reverse Mortgage offering guidance for policymakers aiming to incorporate this tool into broader social and economic policy strategies.

14. Reverse Mortgages: Exploring the Impact of Risk Factors by Source

    Emilia Di Lorenzo, Giulia Magni, Marilena Sibillo

    Abstract

    In recent years, reverse mortgages have gained attention as suitable financial instruments for individuals of retirement age, particularly those classified as “house-rich but cash-poor.” Despite growing interest in countries such as the US, the UK, and Australia, the Italian market remains underdeveloped in this area. From a lender’s perspective, these contracts are perceived as complex, mainly due to the management of various risk components: longevity risk, financial risk, and house price risk. Our goal is to provide lenders with insights into the impact of each risk factor through a time-dependent profit/loss function. This approach aids in identifying the most critical sources of risk, enabling lenders to take appropriate measures to mitigate potential financial threats. We conduct Monte Carlo simulations of the chosen stochastic risk models and apply a single-component VaR assessment procedure. Our findings indicate that house price risk is the most significant risk factor of a Reverse Mortgage portfolio. Moreover, the lender can control the financial risk through the analysis of the risk premium values. The results also highlight that, beyond a certain time horizon, the lender’s exposure stabilizes, with profitability emerging in the long run.

15. Climate Litigation Risk: Comparing Linear and Non Linear Losses of Insurances

    Lorenzo Frattarolo

    Abstract

    We introduce a methodology for quantifying climate litigation risks stemming from insurers’ investment in fossil fuels-related assets. It builds on recent advances in liability attribution of climate warming damages to fossil fuel producers, obtaining the Carbon Majors Index (CMI) as a cumulative emission-weighted portfolio of major polluters’ stocks. We validate the CDI by showing that the percentage of fossil fuel investments is a significant determinant of the yearly exposure to the CMI. We compare linear losses from linear exposures and non-linear losses from Exposure CoVaR. The size of the large polluters’ possible losses from climate litigation is calibrated using losses of Tobacco companies after the US Tobacco Master Settlement Agreement. Our results show that linear and non-linear losses differ in size and ranking of institutions. This suggests the importance of a non-linear long-tail risks approach in assessing climate litigation risk for insurance.

16. Option Hedging Through Reinforcement Learning

    Federico Giorgi, Stefano Herzel, Paolo Pigato

    Abstract

    We propose a Reinforcement Learning algorithm to hedge the payoff of a European call option. The algorithm is first tested on the Black-Scholes-Merton model, where the problem has a well known solution, so that we can compare the strategy obtained by the algorithm to the theoretical optimal one. Then, in a more realistic case that includes transaction costs, the algorithm outperforms the standard delta hedging strategy.

17. Parameter Stability in Yield Curve Fitting

    Lorenzo Mercuri, Andrea Perchiazzo, Edit Rroji, Ilaria Stefani

    Abstract

    We investigate the yield term structure of different countries in order to assess the impact of recent interventions from central banks. We adopt a static approach through the use of the Nelson-Siegel and its extended version named Nelson-Siegel-Svensson model. Empirical results suggest that fitted parameters in the restricted model are more stable across all countries for the period 2020–2025.

18. Deep Learning for Tabular Data: Application to Credit Risk Modeling

    Steven Mphaya, Marialuisa Restaino, Michele La Rocca

    Abstract

    Credit risk is one of the primary risks that banks face, deserving special attention. Previously, modelling credit risk data using parametric models required significant labour, which was time-consuming. Despite the dominance of machine learning (ML) models, deep learning (DL) models for tabular data have emerged to address their drawbacks, including interpretability issues. We seek to determine whether the TabNet model is worth paying the price of its sophisticated computation and interpretability abilities. We used 37991 Italian manufacturing companies to determine their default likelihood. We adopted the Boruta method and sequential attention mechanism for feature selection, SMOTEENN for data balance, and SHAP values to quantify features’ contribution toward model output. A comparative analysis revealed that XGBoost remains a state-of-the-art model in balanced and imbalanced data cases. Thus, leveraging XGBoost can assist lenders in predicting and classifying potential defaulters. Data limitations and feature exclusions set the stage for further exploration of TabNet’s performance in default prediction tasks.

19. Modeling Economic Recovery via Diffusion Processes with Multisigmoidal Logistic Mean Subject to Random Catastrophes

    Sabina Musto, Paola Paraggio

    Abstract

    This work analyzes lognormal diffusion processes with a multisigmoidal logistic mean, subject to random catastrophic events. The occurrence of such catastrophes is governed by a counting process N(t), and upon each catastrophic event, the process restarts from a random state. The resulting process is employed as a model to describe phenomena of an economic and financial nature. In particular, we conduct a simulation study in which the process replicates the dynamics of bank capital, with catastrophes governed by a Poisson process and restart points fixed at the bailout level. Furthermore, we propose an application to real data related to Industrial Production Index (IPI) in which the time arrivals of the catastrophes are fixed and the restart points are binomially distributed. Such application confirms the relevance of the proposed model.

20. Scaling the Tails: Intraday Quantiles for Forecasting Value-at-Risk and Expected Shortfall

    Antonio Naimoli, Ostap Okhrin, Giuseppe Storti

    Abstract

    Incorporating realized volatility measures into risk forecasting models can lead to more accurate forecasts. This paper introduces innovative risk forecasting models that replace realized volatility measures with observable risk proxies derived from high-frequency data through the scaling of intraday quantiles. Specifically, we present a flexible approach for Value-at-Risk and Expected Shortfall forecasting by proposing novel scaling factor estimation methods based on consistent loss functions combined with Multiplicative Error Models using the Generalized F distribution. The empirical analysis across 27 Dow Jones Industrial Average stocks reveals that our proposed approach can achieve significant accuracy improvements in tail risk forecasting.

21. High-Profile GDPR Fines and Their Financial Impact on Listed Firms: An Exploratory Analysis

    Albina Orlando, Serena Pulcini

    Abstract

    This study investigates the short-term market impact of General Data Protection Regulation (GDPR) enforcement actions on publicly listed firms using an event study methodology. In the context of the GDPR’s stringent compliance framework—enforced since May 25, 2018—monetary sanctions act as adverse information signals with potential implications for firm valuation. Focusing on high-profile enforcement cases involving fines exceeding one million euros, this analysis evaluates whether data privacy violations produce statistically significant abnormal returns. The methodology combines a window-based approach, identifying the most sensitive time intervals, with an event-specific analysis that captures heterogeneity in company reactions. A cluster analysis further highlights divergent response patterns, distinguishing firms more exposed to reputation and regulatory risk from those exhibiting greater market resilience. The results offer empirical insights into investor behavior in the face of data protection breaches.

22. Delay-Adjusted Modeling of Cybersecurity Breaches Using INLA: Evidence from State Attorney General Data

    Marco Pirra, Sofia Sarubbo, Fabio Viviano

    Abstract

    This paper presents a statistical framework for analyzing cybersecurity breach data, with a focus on delayed reporting dynamics. Using legally mandated breach notification records from U.S. state attorneys general, we construct a monthly panel of breach occurrences and disclosures for California and Indiana from 2015 to 2025. We implement a Bayesian model with a negative binomial likelihood, incorporating structured temporal, delay-specific, and seasonal effects, and estimate it using Integrated Nested Laplace Approximation (INLA). The model adjusts for reporting lags and enables probabilistic estimation of latent breach incidence. Empirical results reveal significant cross-state differences in breach volume and reporting behavior, underscoring the importance of jurisdiction-specific models. Our findings contribute to the literature on cyber risk forecasting and offer actionable insights for insurers, regulators, and policymakers. The proposed framework supports delay-adjusted risk monitoring and can be extended to additional jurisdictions or enriched with covariates to capture sectoral or organizational heterogeneity.

23. Addressing Long-Term Care Risk Through Pension-Linked Insurance in the Italian Context: A Stochastic Approach Using Severance Pay Scheme

    Alberto Piscitelli

    Abstract

    This paper addresses the growing challenge of long-term care (LTC) dependency in aging populations by proposing the integration of LTC insurance with pension funds through the allocation of severance pay. A stochastic model is introduced to evaluate the financial sustainability and effectiveness of this approach, using Monte Carlo simulations to analyse the trade-offs between pension income and LTC benefits. The findings emphasize the need for welfare reforms and improved health and financial literacy to ensure broader adoption of LTC solutions, contributing to a more sustainable and equitable management of aging-related risks.

24. Backmatter