Intensity-based premium evaluation for unemployment insurance products

•We provide a flexible intensity-based evaluation method for insurance premiums.•We connect F-doubly stochastic Markov chains to estimators of general Cox models.•We give intensity estimates based on a German labor market data set.•We compute unemployment insurance premiums via Monte Carlo simulations.

We present a flexible premium determination method for insurance products, in particular, for unemployment insurance products. The price is determined with the real-world pricing formula and under the assumption that the employment-unemployment progress of an insured person follows an F-doubly stochastic Markov chain. The stochastic intensity processes are estimated for the German labor market, using Cox's proportional hazards model with time-dependent covariates on a sample of integrated labor market biographies. The estimation procedure is based on a counting process framework with stochastic compensators, which we show to be naturally connected to the class of F-doubly stochastic Markov chains. Based on the statistical analysis, the prices are computed using Monte Carlo simulations.