5. Final points
Optimization problem of investment and reinsurance is a very
well established topic. In this paper, we are giving a notable
extension to this set of models by introducing a regime switching
model in which the regime is not directly observable. This reflects
the fact that in reality the nature of the claims might change
over time and this needs to be and can be filtered out from the
observed claims dynamically. Then the main result of the paper is
to identify the optimal reinsurance policies, when we assume that
the insurance firm can also partially hedge its claim in a financial
market and is an exponential utility investor. By analyzing how
the optimal reinsurance policy changes with respect to the safety
loading, we determine the price that the insurance company deems
reasonable for the reinsurance company assuming part of its risk.