  This study investigates an optimal investment problem for an insurance
company operating under the Cramer-Lundberg risk model, where investments are
made in both a risky asset and a risk-free asset. In contrast to other
literature that focuses on optimal investment and/or reinsurance strategies to
maximize the expected utility of terminal wealth within a given time horizon,
this work considers the expected value of utility accumulation across all
intermediate capital levels of the insurer. By employing the Dynamic
Programming Principle, we prove a verification theorem, in order to show that
any solution to the Hamilton-Jacobi-Bellman (HJB) equation solves our
optimization problem. Subject to some regularity conditions on the solution of
the HJB equation, we establish the existence of the optimal investment
strategy. Finally, to illustrate the applicability of the theoretical findings,
we present numerical examples.
