A stochastic approach to insurance cycles

In a series of papers Pentikäinen and coworkers have examined insurance cycles and their consequences for the solvency of insurers and equalization reserves. In a recent contribution, Taylor analyzed the underwriting cycles by means of differential equations, describing more or less deterministic behavior of the cycle. The aim of the present contribution is to give a general framework which can be applied to describe these cycles in a stochastic way. The advantage of our approach lies in the fact that we obtain analytical expressions for solvency margins and that we are able to separate the effects of pure solvency and the effect of cyclic behavior. In other words, a clear distinction is made between the classical idea of solvency and the equalization reserves due to cyclic trends. The underlying idea is from the so-called ‘path integral’, originally arising in quantum mechanics.