Direct use of the empirical quantile function provides a standard distribution-free approach to constructing confidence intervals and confidence bands for population quantiles. We apply this method to construct confidence intervals and confidence bands for regression quantiles and to construct prediction intervals based on sample regression quantiles. Comparison of the direct method with the studentization and the bootstrap methods are discussed. Simulation results show that the direct method has the advantage of robustness against departure from the normality assumption of the error terms.

No abstract

No abstract

In this article, we study the feasibility of dynamic longevity hedging with standardized securities that are linked to broad‐based mortality indexes. On the technical front, we generalize the dynamic “delta” hedging strategy developed by Cairns (2011) to incorporate the situation when population basis risk exists. On the economic front, we discuss the potential financial benefits of an index‐based hedge over a bespoke risk transfer. By considering data from a large group of national populations, we find evidence supporting the diversifiability of population basis risk. We further propose a customized surplus swap—executed between a hedger and reinsurer—to utilize the diversifiability. As standardized instruments demand less illiquidity premium, a combination of a dynamic index‐based hedge and the proposed customized surplus swap may possibly be a more economical (and equally effective) alternative to a bespoke risk transfer.

Summary Stochastic mortality models have a wide range of applications. They are particularly important for analysing Chinese mortality, which is subject to rapid and uncertain changes. However, owing to data‐related problems, stochastic modelling of Chinese mortality has not been given adequate attention. We attempt to use a Bayesian approach to model the evolution of Chinese mortality over time, taking into account all of the problems associated with the data set. We build on the Gaussian state space formulation of the Lee–Carter model, introducing new features to handle the missing data points, to acknowledge the fact that the data are obtained from different sources and to mitigate the erratic behaviour of the parameter estimates that arises from the data limitations. The approach proposed yields stochastic mortality forecasts that are in line with both the trend and the variation of the historical observations. We further use simulated pseudodata sets with resembling limitations to validate the approach. The validation result confirms our approach's success in dealing with the limitations of the Chinese mortality data.