Modeling Longevity Risk using Extreme Value Theory: An Empirical Investigation using Portuguese and Spanish Population Data

Extreme value theory (EVT) provides a framework to formalize the study of behaviour in the tails of a distribution. In this paper we use EVT to model the statistical behaviour of mortality rates over a given high threshold age and to estimate the significance of rare longevity risk in a given population. We adopt a piecewise approach in estimating the optimal threshold age using an iterative algorithm of maximum likelihood estimation.that statistically determines the cut-off between the central (Gompertz) part of the distribution and the upper tail modelled using the generalized Pareto distribution. The model is empirically tested using the most recent period mortality data for the total, male and female populations of Portugal and Spain. We use some classical results from EVT to estimate the evolution of the theoretical maximum life span over time and to derive confidence intervals for the central estimates. We then use time series methods to forecast the highest attained age. We observe a good fit of the model in all populations and subperiods analysed and on the whole life span considered. We estimate an increase in the theoretical maximum life span over time for all populations, more significant in the male subpopulations

Mortality and Longevity Projections for the Oldest-Old in Portugal

The mortality decline observed in developed countries over the last decades significantly increased the number of those surviving up to older ages. Mortality improvements are naturally viewed as a positive change for individuals and as a substantial social achievement for societies, but create new challenges in a number of different areas, ranging from the planning of all components of social security systems to labour markets. Understanding mortality and survival patterns at older ages is crucial. In this paper, we compare the results provided by a number of different methods designed to project mortality for the oldest-old in the Portuguese population. We identify the merits and limitations of each method and the consequences of their use in constructing complete life tables

Prospective Lifetables: Life Insurance Pricing and Hedging in a Stochastic Mortality Environment

In life insurance, actuaries have traditionally calculated premiums and reserves using a deterministic mortality intensity, which is a function of the age of the insured only. Over the course of the 20th century, the population of the industrialized world underwent a major mortality transition, with a dramatic decline in mortality rates. The mortality decline has been dominated by two major trends: a reduction in mortality due to infectious diseases affecting mainly young ages, and a decrease in mortality at old ages. These mortality improvements have to be taken into account to price long-term life insurance products and to analyse the sustainability of social security systems. In this paper, we argue that pricing and reserving for pension and life insurance products requires dynamic (or prospective) lifetables. We briefly review classic and recent projection methods and adopt a Poisson log-bilinear approach to estimate Portuguese Prospective Lifetables. The advantages of using dynamic lifetables are twofold. Firstly, it provides more realistic premiums and reserves, and secondly, it quantifies the risk of the insurance companies associated with the underlying longevity risks. Finally, we discuss possible ways of transferring the systematic mortality risk to other parties.

Parametric interest rate risk immunization

In this chapter we develop a new immunization model based on a parametric specification of the term structure of interest rates. The model extends traditional duration analysis to account for both parallel and non-parallel term structure shifts that have an economic meaning. Contrary to most interest rate risk models, we formally analyse both first-order and second-order conditions for bond portfolio immunization, emphasizing that the key to successful immunization will be to build up a portfolio such that the gradient of its future value is zero, and such that its Hessian matrix is positive semidefinite. We provide explicit formulae for new parametric interest rate risk measures and present alternative approaches to implement the immunization strategy. Additionally, we develop a more accurate approximation for the price sensitivity of a bond based upon new parametric interest rate risk measures and revise both classic and modern approaches to convexity in order to highlight the risks of convexity when changes other than parallel shifts in the term structure are considered. Furthermore, we provide useful expressions for the sensitivity of interest rate risk measures to changes in term structure shape parameters

Tunable and robust long-range coherent interactions between quantum emitters mediated by Weyl bound states

Long-range coherent interactions between quantum emitters are instrumental for quantum information and simulation technologies, but they are generally difficult to isolate from dissipation. Here, we show how such interactions can be obtained in photonic Weyl environments due to the emergence of an exotic bound state whose wavefunction displays power-law spatial confinement. Using an exact formalism, we show how this bound state can mediate coherent transfer of excitations between emitters, with virtually no dissipation and with a transfer rate that follows the same scaling with distance as the bound state wavefunction. In addition, we show that the topological nature of Weyl points translates into two important features of the Weyl bound state, and consequently of the interactions it mediates: first, its range can be tuned without losing the power-law confinement, and, second, they are robust under energy disorder of the bath. To our knowledge, this is the first proposal of a photonic setup that combines simultaneously coherence, tunability, long-range, and robustness to disorder. These findings could ultimately pave the way for the design of more robust long-distance entanglement protocols or quantum simulation implementations for studying long-range interacting systems

Longevity-Linked Life Annuities: A Bayesian Model Ensemble Pricing Approach

Participating longevity-linked life annuities (PLLA) are an interesting solution to manage systematic longevity risk in markets in which alternative risk management solutions are scarce and/or expensive and in which there are significant demand- and supply-side constraints that prevent individuals from annuitizing their retirement wealth. In this paper we revisit, complement and expand previous research on the design, valuation and willingness to pay for various index-type PLLA structures. Contrary to previous studies that use a single model to forecast mortality rates, we develop a novel approach based on a Bayesian Model Ensemble of generalised age-period-cohort stochastic mortality models. To determine which models received a greater or lesser weight in the final projections, we implemented a backtesting cross-validation approach. We use Taiwan (mortality, yield curve and stock market) data from 1980 to 2019 and adopt a longevity option decomposition valuation approach. The empirical results provide significant valuation and policy insights for building post-retirement income, particularly in Asian countries