We study solvency of insurers in a comprehensive model where various economic factors affect the capital developments of the companies. The main interest is in the impact of real growth to ruin probabilities. The volume of the business is allowed to increase or decrease. In the latter case, the study is focused on run-off companies. Our main results give sharp asymptotic estimates for infinite-time ruin probabilities.

We study solvency of insurers in a practical model where in addition to basic insurance claims and premiums, economic factors like inflation, real growth and returns on the investments affect the capital developments of the companies. The objective is to give qualitative descriptions of risks by means of crude estimates for finite time ruin probabilities. In our setup, the economic factors have a dominant role in the estimates. In addition to this theoretical view, we will focus on applied interpretations of the results by means of discussions and examples.

The first version of the paper was presented in ASTIN Colloquium in Helsinki 2009. The colloquium was dedicated to Teivo Pentikäinen.