  In this work we investigate the optimal proportional reinsurance-investment
strategy of an insurance company which wishes to maximize the expected
exponential utility of its terminal wealth in a finite time horizon. Our goal
is to extend the classical Cramer-Lundberg model introducing a stochastic
factor which affects the intensity of the claims arrival process, described by
a Cox process, as well as the insurance and reinsurance premia. Using the
classical stochastic control approach based on the Hamilton-Jacobi-Bellman
equation we characterize the optimal strategy and provide a verification result
for the value function via classical solutions of two backward partial
differential equations. Existence and uniqueness of these solutions are
discussed. Results under various premium calculation principles are illustrated
and a new premium calculation rule is proposed in order to get more realistic
strategies and to better fit our stochastic factor model. Finally, numerical
simulations are performed to obtain sensitivity analyses.
