Solvency of the insurer and incomplete financial markets
We investigate solvency of insurers when liabilities are financed by a stream of assets. The term structure of interest rates and the streams of assets and liabilities are assumed to be random, with a risk-switching mechanism which enables a better modelling of insurer's claims. It is of special importance in practice since tornados, floods, earthquakes and other extreme events can rapidly cause a significant increase in large insurance claims. Stability of the insurer's portfolio against the interest rate risk is also treated. New tools for bounding the changes in the portfolio surplus in response to changes in the term structure of interest rates are investigated as well as bounds for important insolvency risk measures in a risk-switching model and in its generalization.