Modeling and Estimation of Stochastic Transition Rates in Life Insurance with Regime Switching Based on Generalized Cox Processes

In this paper we aim at modeling stochastic transition rates of state processes in life insurance by using generalized Cox processes. A feature of a our non-Gaussian model is that it can be used to capture 'regime switching' effects of data which may be due to regulatory changes in insurance markets or external 'shocks' caused e.g. by an economical crisis, natural disasters or epidemics. We propose a method how to estimate the unknown parameters of our model for stochastic transition rates from insurance data by using non-linear filtering techniques for Levy processes. As a result we also obtain an explicit formula for the unnormalized density of a filtering problem with singular coefficients.