Fabio Viviano

Comparison of predictors' performance in insurance pricing: Testing for Bregman dominance based on Murphy diagrams Ehm et al. (2016) defined forecast dominance, or Bregman dominance as dominance for every Bregman loss function. This letter explores Bregman dominance to compare competing candidate pure premiums. An actuarial interpretation is given for the expectation of extremal consistent loss functions characterizing Bregman dominance, showing their relevance in the context of insurance pricing. An effective testing procedure for Bregman dominance is proposed based on Murphy diagrams and its performance is evaluated through a simulation study. Compared to the existing literature, the proposed testing procedure is easier because it exploits the independence and homogeneity assumptions made in insurance studies and focuses on the conditional mean. An application to a Swiss motor insurance data set demonstrates the potential of the proposed procedure. Participating life insurances in an equity-Libor market model This article introduces an equity-LIBOR Market Model (LMM) that integrates the investment strategy into the valuation process of participating life insurance policies. Within this framework, we consider bond portfolios rebalanced across multiple maturities and provide a semi-analytical formula for approximating the fair value of liabilities. We then investigate the impact of the investment policy on the net asset value and the Solvency Capital Requirement. To carry out this analysis, we propose a Monte Carlo method for generating sample paths under both LIBOR and real measures, alongside an estimation procedure under the real measure. The numerical illustration focuses on the asset-liability management of an endowment and a life annuity. Covid-19 mortality: the Proportionality Hypothesis We introduce and provide evidence to support the Proportionality Hypothesis which states that Covid-19 infection fatality rates are approximately proportional to all-cause death rates by age and subgroup (e.g., socio-economic class). We also show that vaccination played a very significant role in preventing people infected with Covid-19 from needing to be hospitalised, since it reduced the average severity of an infection. Death rates involving Covid-19 were very significantly lower for people in the fully vaccinated group compared to the unvaccinated group. During the pandemic, death rates from other causes were in some cases reduced (e.g., flu and pneumonia), in some cases unchanged (e.g., lung cancer) and in some cases elevated (e.g., heart disease). We discuss the implications of our findings both for potential adjustments to extrapolative mortality models which allow for future pandemics in a way that is consistent with the Proportionality Hypothesis and for insurance companies in terms of both modelling extreme scenarios and the design of mortality catastrophe bonds. An iterative least-squares Monte Carlo approach for the simulation of cohort based biometric indices This paper tackles the problem of approximating the distribution of future biometric indices under a cohort-based perspective. Unlike period-based evaluations, cohort-based schemes require the computation of conditional expectations for which explicit solutions often do not exist. To overcome this issue, we suggest the application of a well-established methodology, i.e., the Least-Squares Monte Carlo approach. The idea is to approximate conditional expectations by combining simulations and regression techniques, thus avoiding a straightforward but computationally demanding nested simulations method. To show the extreme flexibility and generality of the proposal, we provide extensive numerical results concerning two main longevity indices, life expectancy and lifespan disparity, obtained by adopting both single- and multi-population mortality models. Comparisons between period- and cohort-based results are made as well. Finally, the paper shows that the proposed methodology can be used to approximate other biometric indices at future dates for which cohort-based estimations are often replaced by period ones for computational simplicity. Actuarial aspects of subjective survival probabilities with applications in insurance pricing Subjective survival probabilities reflect individuals’ views about own future survival and they vary based on socio-demographic factors. Actuaries and demographers use parametric survival models, often calibrated on population mortality data, to capture and interpret mortality trends. Recent research highlights the importance of considering subjective survival beliefs in mortality studies. In the same spirit, this work aims to evaluate the applicability of subjective survival probabilities in insurance pricing. More specifically, the proposed methodology focuses on the construction of subjective survival tables for pricing insurance products based on various parametric modelling approaches. Our results indicate that subjective survival probabilities contain information useful for predicting actual mortality and pricing life insurance products for the U.S. population.

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.

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.