Mortality density forecasts: An analysis of six stochastic mortality models

This paper develops a framework for developing forecasts of future mortality rates. We discuss the suitability of six stochastic mortality models for forecasting future mortality and estimating the density of mortality rates at different ages. In particular, the models are assessed individually with reference to the following qualitative criteria that focus on the plausibility of their forecasts: biological reasonableness; the plausibility of predicted levels of uncertainty in forecasts at different ages; and the robustness of the forecasts relative to the sample period used to fit the model. An important, though unsurprising, conclusion is that a good fit to historical data does not guarantee sensible forecasts. We also discuss the issue of model risk, common to many modelling situations in demography and elsewhere. We find that even for those models satisfying our qualitative criteria, there are significant differences among central forecasts of mortality rates at different ages and among the distributions surrounding those central forecasts.     

Nucleon decay in supersymmetric models via gluino dressed graphs

Dimension-five baryon-number-violating operators may contribute to proton decay via gaugino exchange, which converts then to the usual dimension-six operators. We show that gluino-exchange contributions may be expected to dominate for a large top quark mass (m_t > 40 GeV). In this case the dominant decay modes are $\text{p → K}{}^0\text{μ}{}^{\mathrm{+}}\text{, K}{}^{\mathrm{+}}\text{ν}\text{and}\text{n →}\text{ν}\text{K}{}^0\text{, μ}{}^{\mathrm{+}}\text{π}{}^{\mathrm{?}}\text{, K}{}^0\text{π}{}^{\mathrm{?}}\text{μ}{}^{\mathrm{+}}$. We also estimate the decay lifetime.     

The Z-transform and linear multistep stability

^** Email: mapjjc{at}maths.bath.ac.uk^*** Corresponding author. Email: ath{at}maths.bath.ac.uk^**** Email: hl{at}maths.bath.ac.uk This paper makes systematic use of control-theoretic methodssuch as the -transform, small-gain theorems and frequency-domainstability criteria in the analysis of the stability behaviourof linear multistep methods. Some of the results in Nevanlinna'swork are recovered and a number of new boundedness and asymptoticproperties of solutions of numerical schemes are obtained. Inparticular, we give a careful and detailed analysis of the nonlinearstability properties of strictly zero-stable methods.