Importance sampling for actuarial cost analysis under a heavy traffic model

Abstract

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.