A heavy traffic approach to modeling large life insurance portfolios

- We propose a bottom-up approach to model large life insurance portfolios.
- We use heavy-traffic approximation to derive and justify the structure of the risk processes.
- The risk processes are shown to depend on mortality and insurance contract structure in a tractable manner.
- We formulate and compute ruin probability that takes actuarial reserve into account.
- We identify explicitly the temporal and cross-sectional correlation structure of the derived risk processes.

We explore a new framework to approximate life insurance risk processes in the scenario of plentiful policyholders, via a bottom-up approach. Given the insurance contract structure, we aggregate the balance of individual policy accounts, and derive an approximating Gaussian process with computable correlation structure. The methodology is borrowed from heavy traffic theory in the literature of many-server queues, and involves the so-called fluid and diffusion approximations. Our framework is different from the individual risk model in that it takes into account the time dimension and the specific policy structure including the premium payments. It is also different from classical risk theory in that it builds the risk process from micro-level contracts and parameters instead of assuming aggregated claim and premium processes outright. As a result, our approximating process behaves differently depending on the issued contract structure. We also illustrate the flexibility of our approach by formulating a finite-horizon ruin problem that incorporates actuarial reserve in the consideration.