This paper provides an econometric analysis aiming at evidencing the dynamics showed by the S&P 500 market index during the period of 4 January 2001–28 April 2020, in which the subprime crisis has taken place and the COVID-19 crisis has begun. In particular, we fit a three-regime switching model that allows market parameters to behave differently during economic downturns, with the regimes representative of the tranquil, volatile, and turbulent states. We document that the tranquil regime is the most frequent for the whole period, while the dominant regime is the volatile one for the crisis of 2008 and the turbulent one for the first four months of 2020. We fit the same model to the returns of the Dow Jones Industrial Average index and find that during the same period of investigation, the most frequent regime has been the tranquil one, while the volatile and turbulent regimes share the same frequencies. Additionally, we use a multinomial logit model to describe the probabilities of volatile or turbulent regimes. We show that, in the case of the S&P 500 index, the returns from the Volatility Index (VIX) index are significant for both the volatile and the turbulent regimes, while the gold, WTI oil, and the dollar indices have some explanatory power only for the turbulent regime.

We propose a direct non-parametric estimation framework for multi-state disability models that does not rely on the Markov assumption. In this context, “direct” denotes a method that does not necessitate the initial estimation of transition intensities. Previous research has demonstrated evidence of non-Markovian properties in disability dynamics, and a number of studies have employed semi-Markov models for Long-Term-Care products. We test the non-Markov assumption on an up-to-date American dataset that includes more than 200,000 records, finding insights on the non-Markovian character of disability. We then focus on transition probabilities, showing the impact of our assumption on these crucial metrics for actuaries. In addition, we investigate the influence of health conditions on all the transitions analyzed.

Cyber risks and particularly data breaches constitute one of the new frontiers of risk modeling for insurers across the world. We use the cointegration methodology to uncover the relation between data breaches and Bitcoin-related variables. We perform our analyses on two different datasets of data breaches. In both cases, we provide statistical evidence of a bidirectional lead–lag relation in the short run between the variables under investigation. Moreover, the existence of a cointegrating vector suggests that this relation is likely to persist in the long run. To evaluate the quantitative implications of the relations found, we complement the study with Granger causality tests, impulse response analyses and variance decompositions of the forecasting errors.

We use recent advances in polynomial diffusion processes to develop a continuous-time joint mortality model for the actuarial valuation and risk analysis of life insurance liabilities. The model considers the stochastic nature of future mortality improvements and introduces a common subordinator for the marginal survival processes, resulting in a nontrivial dependence structure between the survival of pairs of individuals. Polynomial diffusion processes can be used to derive closed-form formulae for standard actuarial quantities. The model fits well with a classic dataset provided by a Canadian insurer and can be used to evaluate products issued to multiple lives, as shown through numerical applications.

The aim of this paper is to employ explainable artificial intelligence methods to prioritize cyber risks. To achieve this, we compare alternative machine learning models that predict the evolution of cyber attacks while accounting for time dependence. Subsequently, we apply explainable AI techniques to identify the most significant types of cyber attacks based on their occurrence. We illustrate our approach using data from the Hackmanac website, which categorizes worldwide cyber attacks by severity. The empirical findings reveal two distinct periods: before and after 2023. In both cases, eXtreme Gradient Boosting emerges as the best-performing model. Furthermore, the most relevant explanatory features remain relatively consistent across different explainable artificial intelligence methods but vary over time, reflecting the recent evolution of cyber threats.