On a Surplus Process under a Periodic Environment: a Simulation Approach

The problem of modeling claims occurring in periodic random environments is discussed in this paper. In the classical approach of risk theory, the occurrence of claims is modeled by counting processes that do not account for claims following a periodic pattern. The author discusses how the use of the classical approach to model a periodic portfolio might lead to the miscalculation of important risk indices, namely the associated ruin probability. He presents a periodic model, in terms of nonhomogeneous Poisson processes, that has potential practical applications. The discussion is based on some properties of the modeled periodic intensities. Existing simulation techniques are adapted to this periodic model, which provides a practical way to evaluate ruin probabilities.