Lee ir Carterio mirtingumo prognozavimo modelis ir jo modifikacijos draudimo įmonės mokumui skaičiuoti

Risk capital models are widely applied by insurance companies both for the solvency assessment and for risk management. The main topics of the dissertation are the development of models used for assessment of Value-at-Risk for mortality risk and calculation of the related mortality projections. When calculating the Value-at-Risk for mortality risk stochastic mortality projections are used as an input. For the purpose of generation of the projections we develop the classical Lee-Carter model, the modification of this model derived using Poisson regression, and Lee-Cater model modifications derived using state space models. The state space Lee-Carter models, linear state space model and state space model with regime switching, allow us to take into account a change in mortality trend and to consider changes of mortality variance in time. For estimation of state space model parameters, we applied Gibbs sampler, which is one of Markov Chain Monte Carlo methods. The calculated mortality projections are used for calculation of Value-at-Risk for mortality risk using two different methods: one-year VaR and run-off VaR. The application of the methods was illustrated using empirical mortality data of Lithuania and Sweden.