We propose a new model in a Bayesian hierarchical framework to project mortality at both national and subnational levels based on sparse or missing data. The new model, which has a country-region-province structure, uses common factors to pool information at the national level and within regions...

Expected shortfall (ES) is a popular risk measure and plays an important role in risk and portfolio management. Recently, change-point detection of risk measures has been attracting much attention in finance. Based on the self-normalized CUSUM statistic in Fan, Glynn and Pelger (2018) and the...