A set of new stochastic trend models

A set of new stochastic trend models


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Speaker: Johannes Schupp

Due to the observed and persistently strong improvements in life expectancy, the estimation of future mortality improvements and trends by actuaries and demographers gains more and more social and financial importance. Often, (stochastic) forecasting is performed by means of parametric mortality models, e.g. the models of Lee and Carter (1992), Cairns et al. (2006), or Plat (2009) that reduce the puzzle of mortality to a few interpretable parameters.

Typically a random walk with drift is used to project the time dependent parameters within such models. However, in some cases it seems to underestimate the uncertainty in future mortality rates due to its constant and fixed drift (see Börger et al. (2014) or Lee and Miller (2001)). Clearly, this is critical whenever forecasts of mortality are used for the pricing of longevity derivatives.

In many countries, historic mortality trends seem to have followed a piecewise linear trend whose slope changes once in a while (see Sweeting (2011), Li et al. (2011), Börger and Schupp (2015)). In this paper, we propose a set of new likelihood based trend processes as we further develop earlier approaches for the calibration of a trend process within a consistent stochastic framework that builds on the patterns in historic mortality. Within the calibration of the trend model, we implicitly derive the distribution of the future trend process. Hereby, future projections are highly consistent to historic observations. Often, mortality is characterized by one-year or multi-year changes due to exogenous factors, e.g. pandemia. We address these historic effects with a variety of trend models accounting for outliers, heteroscedasticity and seasonal structures.

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