The purpose of this article is to investigate whether considering stylized facts in financial time series leads to better estimation of risk measures. This study focuses on long-memory GARCH-type models chosen for their ability to capture characteristics of financial time series like long memory and volatility clustering. There are periods of high and low volatility in financial markets. One of the most important ways to reduce risk is to use a time-series model to manage market risk. In comparison to long-memory GARCH-type models, such as fractionally integrated generalised autoregressive conditional heteroskedasticity and hyperbolic generalised autoregressive conditional heteroskedasticity, this research study aims to determine how effective the fractionally integrated asymmetric power autoregressive conditional heteroskedasticity is at producing competitive risk measures. The stock returns are assumed to follow a family of extreme parametric distributions in long-memory GARCH-type models. The historical closing price time series for both short and long trading positions on the various confidence levels correspond to the left and right quantiles of the return distributions, respectively. The findings show that FIAPARCH with Student's-t distribution has a high chance of becoming a suitable model for generating reliable risk measures. However, FIGARCH fits the data well to generate risk measures when using the presumptive skewed Student's-t distribution model.

Cryptocurrency markets have experienced repeated systemic breakdowns over the past decade, exposing structural fragilities within digital asset ecosystems. Prominent examples include the Mt. Gox collapses (2011–2014), the COVID-19-driven “312” flash crash, the “519” crash in 2021 following environmental concerns, the 2017–2018 crypto winter, the collapse of the Terra/Luna ecosystem and the FTX exchange in 2022, and the combined effects of Grayscale ETF outflows and tariff conflicts in early 2025. These disruptions were driven by regulatory shocks, exchange failures, excessive leverage, macroeconomic instability, and automated liquidation cascades, often producing billions in losses within hours and erasing trillions in market capitalization. This study proposes a mathematical framework for diagnosing cryptocurrency market failures through the decomposition of financial time-series data. The approach integrates nonlinear signal analysis with regime-shift detection techniques to identify critical transitions preceding major breakdown events. Empirical examination of multiple crisis episodes reveals consistent precursory signatures, including structural changes in volatility dynamics, distortions in trading flows, and abnormal amplitude fluctuations in price signals. These indicators provide insight into latent systemic instability and suggest the feasibility of early diagnostic signals for emerging market stress. The proposed framework contributes a quantitative perspective for analyzing crypto-market fragility and offers analytical tools for examining complex, chaotic behaviors that remain inadequately captured by conventional financial risk metrics.

Longevity risk represents a structural source of uncertainty for modern pension systems and longevity-linked financial arrangements. Under persistent mortality improvements, period life expectancy evaluated at retirement age systematically understates the effective lifetime of real cohorts, generating a wedge between period and cohort measures. The magnitude and dynamics of this Life Expectancy Gap (LEG) depend critically on how future mortality rates are projected, since cohort life expectancy aggregates mortality along the diagonal of the Lexis surface and is therefore inherently forward-looking.

This paper investigates how model uncertainty and forecast combination design affect the measurement of cohort-based longevity indicators and the implied intergenerational transfers embedded in pension rules. Rather than proposing a new structural mortality specification, we focus on the aggregation layer within the class of generalized age–period–cohort (GAPC) mortality models. We implement a horizon-specific stacked regression ensemble (SRE), where combination weights are estimated via blocked time-series cross-validation and allowed to vary across forecasting horizons. This approach explicitly targets multi-step predictive risk and accounts for the instability of model performance across horizons.

To interpret the sources of predictive gains, we introduce a cooperative game–theoretic attribution based on the Shapley value. For each forecasting horizon, Shapley values provide an axiomatically grounded decomposition of out-of-sample risk reduction relative to an equal-weight benchmark, linking ensemble weights to the marginal informational contribution of each mortality specification.

Using Italian mortality data from the Human Mortality Database for ages 60–100 over 1960–2022, we construct extended mortality surfaces to compute period and cohort life expectancy at retirement age and the associated longevity gap. Results show that while a positive cohort–period wedge is robust across aggregation schemes, its magnitude and long-run dynamics differ materially between horizon-adaptive stacking and static forecast averaging, implying non-trivial consequences for the measurement of intergenerational transfers and actuarial fairness in pension systems.

Introduction

The recent increase in life expectancy, while reflecting improvements in living standards, implies long retirement periods, high long-term care expenses and pressure on the pension system. The elderly often hold valuable real estate assets but lack the liquidity to face the demands of consumption needs and medical expenses (house-rich and cash-poor). In this framework, Reverse Mortgage (RM) may constitute a valid financial support: it allows elder homeowners to borrow money against their home while maintaining the right to live in it. Upon the borrower’s death, heirs must repay the debt, and the non-negative equity guarantee ensures that the exceed of the proceeds of the sale of the property is transferred to the heirs. Despite its availability in Italy, RM remains relatively underutilized. In this study, we provide useful insights into the Italian RM market and investigate the reasons behind its limited adoption.

Methods

We present a twofold analysis. First, we construct a life-cycle model to evaluate the borrower’s decision problem, taking into account long-term care expenses and house maintenance costs. Exploiting a dynamic programming technique, we establish the optimal saving streams with and without RM. We then perform a comprehensive quantitative analysis conducted among potential Italian subscribers to assess current levels of awareness and to identify the factors hindering access to this credit line.

Results

The life-cycle model approach shows that elders receive higher utility gains when using RM. Under three different health scenarios, the liquid wealth available in the case of RM was shown to alleviate the pressure on the elders’ savings. The survey results underline elders’ trust issues with respect to the institutions that offer RM. Product complexity and emotional attachment to the property are among the main factors hindering the development in the uptake of this option.

Conclusions

Our work highlights the main criticalities affecting RM in the Italian market and provides relevant policy indications to enhance the potentiality of this product.

Risk transfer mechanisms increasingly rely on instruments whose payoffs are imperfectly aligned with the underlying exposures they are intended to hedge.

This misalignment generates basis risk and complicates the evaluation of optimal coverage decisions for insurers. Understanding how insurers determine the appropriate level of coverage when hedging effectiveness is limited therefore represents a relevant problem in insurance risk management.

This work develops a stylized analytical framework to study the insurer’s optimal risk transfer decision in the presence of imperfect hedging.

The insurer faces a stochastic loss process and can transfer risk through an external instrument whose payoff is only partially correlated with the underlying exposure. The effectiveness of the hedge is therefore driven by the statistical relationship between the loss process and the hedging instrument.

The insurer’s decision problem is modeled as a trade-off between risk reduction and expected profitability. Risk mitigation is achieved by transferring part of the exposure, while expected profitability is constrained by an endogenous minimum profit requirement reflecting managerial preferences and business sustainability considerations.

Within this setting, the model characterizes the optimal level of coverage as a function of hedge effectiveness, pricing conditions, and the insurer’s tolerance for residual risk. The analysis highlights how imperfect hedging generates distinct coverage regimes and may lead insurers to adopt partial risk transfer even when hedging instruments are available.

The framework provides a simple analytical structure that helps interpret heterogeneous coverage choices observed in practice.

Introduction:
The increasing frequency and severity of extreme precipitation events pose significant challenges for the insurance industry in quantifying and managing climate-related economic losses. This study develops a statistical–actuarial framework to estimate the distribution of economic losses conditional on extreme precipitation levels. The approach integrates heavy-tailed marginal modeling with copula-based dependence structures, allowing the joint behavior of meteorological extremes and disaster losses to be analyzed within a coherent probabilistic setting.

Methods:
To model the marginal behavior of precipitation and loss variables, we assess a range of right‑skewed candidate distributions, including those with heavy fat tails. Dependence between precipitation and losses is captured using Gaussian, t-Student, and Gumbel copulas. Conditional loss quantiles, including Value at Risk (VaR), are estimated under different precipitation scenarios. Weekly maximum precipitation data from Spain (2018–2025) and economic loss records from the Emergency Events Database (EM-DAT) for selected European countries and the NOAA Storm Events Database for the United States are used for empirical illustration.

Results:
The results show that specifications incorporating upper-tail dependence generate substantially higher conditional Value at Risk estimates than symmetric Gaussian dependence, particularly in the United States, where extreme losses dominate the distribution.

Conclusions:
The proposed framework provides a flexible and robust tool for climate risk assessment, supporting insurers and policymakers in capital allocation, pricing, and disaster risk management under extreme weather conditions.

Extreme price episodes such as bubbles and crashes are pervasive in cryptocurrency markets. While a growing body of literature has examined these phenomena in major cryptocurrencies, relatively few studies have investigated their presence and implications for stablecoins, whose prices are designed to maintain a relatively stable value compared to other cryptocurrencies. Moreover, the role of extreme events in volatility modeling and their spillover effects across digital assets remain relatively underexplored. To address this gap, this study employs the Bubble Crash-GARCH (BC-GARCH) model, which allows us to explicitly incorporate extreme price events into volatility modeling through the Phillips, Shi, and Yu (PSY) test. The detected bubble and crash episodes are included as dummy variables in the conditional mean equation of returns. The empirical analysis considers major cryptocurrencies such as Bitcoin and Ethereum together with the stablecoin Tether, and is conducted under several GARCH-type volatility specifications. Contagion effects are also investigated by incorporating Bitcoin bubble and crash signals into the volatility models of other digital assets. The BC-GARCH specification reduces the latent component of the data generating process and enhances volatility forecast accuracy relative to standard GARCH benchmarks. Moreover, extreme events in Bitcoin provide informative signals for the volatility dynamics of other cryptocurrencies.

Introduction: This systematic review examines the influence of Prospect Theory (PT) across finance, management, and psychology. By analyzing literature along two dimensions—scholarly stance toward the theory and its functional contributions—this study provides a novel, common framework to measure and compare PT’s impact across diverse academic fields.

Methods: Following PRISMA 2020 guidelines, the Web of Science database was searched for "prospect theory" or "loss aversion" (1979–2024). To assess methodological quality and perform a high-impact synthesis, a purposive sampling strategy was employed—inspired by Holmes et al. (2011)—where only the top 25 most-cited articles from predetermined prestigious journals were screened to reflect scholarly consensus. Eligibility required a direct application of PT or Cumulative Prospect Theory. Google Scholar identified additional records. For the first dimension (scholarly stance), a standardized coding protocol was used: studies fully affirming PT received 1 point, while partial affirmations received 0.5 points. For the second dimension (contributions), studies were categorized as "theory building" or "explanation of a concept." A qualitative and quantitative synthesis was performed. This review was not registered.

Results: The final review included 55 articles: 27 in management, 16 in finance, and 12 in psychology. Scholarly affirmation scores were 16.5 for management, 10 for finance, and 7 for psychology, while rejection scores were 4.5, 5, and 2, respectively. Regarding functional contributions, PT was utilized for theory building in 12 management, 6 finance, and 6 psychology studies. Conversely, PT was used for conceptual explanation in 12 management, 7 finance, and 4 psychology studies.

Conclusions: This review demonstrates a predominantly affirmative scholarly stance toward PT, ranging from 66.67% to 78.57% across disciplines. Furthermore, PT's contributions are nearly equally distributed between theory building and conceptual explanation across all three fields.

Rising life expectancy is reshaping retirement systems and may have important implications for pension funds’ long-term investment strategies. While traditional life-cycle models predict a gradual reduction in equity exposure as plan members age, rising life expectancy may instead extend investment horizons and increase the resources required to finance retirement consumption. As individuals live longer and spend more years in retirement, pension funds may face stronger incentives to seek higher long-term returns in order to sustain future pension liabilities. This paper explores the relationship between longevity and pension funds’ asset allocation, focusing on the share of financial assets invested in equities. Using cross-country data for a sample of OECD countries, we examine whether improvements in life expectancy are associated with changes in pension funds’ investment behavior. The analysis also considers the role of demographic dynamics, macroeconomic conditions, and differences in financial systems in shaping this relationship. Our findings suggest that longevity trends may influence pension funds’ willingness to allocate a larger share of their portfolios to return-seeking assets. At the same time, the strength of this relationship appears to depend on institutional features and market conditions, highlighting the importance of the broader financial environment in shaping long-term investment strategies. Overall, the study contributes to the growing debate on how demographic change affects institutional investors and long-term capital allocation. The results also provide relevant insights for pension system design and regulatory frameworks, as well as for policies aimed at supporting long-horizon investment and capital market development.

Accurate modeling of mortality rates is crucial for effective risk management. It affects product pricing, reserving, and capital estimation. Modeling mortality experience for insurance portfolios is particularly challenging in emerging markets, where data is often limited and inconsistent.

This research introduces a hybrid modeling framework that integrates actuarial graduation with tree-based machine learning models to enhance the modeling and forecasting of insurance mortality rates.

The proposed framework first applies graduation models, including the Makeham law and P-splines, to smooth crude mortality rates and capture underlying patterns. Tree-based machine learning models, including decision trees, random forests, and gradient boosting, are then utilized with two splitting approaches, random splitting and year-based splitting, to estimate and forecast graduated mortality rates, capturing nonlinear dependencies across age, year, and gender.

The methodology is applied to Egyptian life insurance data covering ages 16 to 60 for the period 2013 to 2019. The empirical results showed that the Makeham model provides a better fit and higher predictive accuracy for graduating mortality rates. Among machine learning models, gradient boosting with both random and year-based splitting achieves the highest predictive accuracy and supports reliable prediction of future mortality rates.

By combining the interpretability of actuarial graduation methods with the predictive capability of machine learning, the proposed framework provides a robust approach for modeling and forecasting insurance mortality rates in life insurance applications.