Importance sampling for actuarial cost analysis under a heavy traffic model

We explore a bottom-up approach to revisit the problem of cash flow modeling in insurance business, and propose a methodology to efficiently simulate the related tail quantities, namely the fixed-time and the finite-horizon ruin probabilities. Our model builds upon the micro-level contract structure issued by the insurer, and aims to capture the bankruptcy risk exhibited by the aggregation of policyholders. This distinguishes from traditional risk theory that uses random-walk-type model, and also enhances risk evaluation in actuarial pricing practice by incorporating the dynamic arrivals of policyholders in emerging cost analysis. The simulation methodology relies on our model´s connection to infinite-server queues with non-homogeneous cost under heavy traffic. We will construct a sequential importance sampler with provable efficiency, along with large deviations asymptotics.