Optimal investment for insurers

We consider a risk process modelled as a compound Poisson process. The ruin probability of this risk process is minimized by the choice of a suitable investment strategy for a capital market index. The optimal strategy is computed using the Bellman equation. We prove the existence of a smooth solution and a verification theorem, and give explicit solutions in some cases with exponential claim size distribution, as well as numerical results in a case with Pareto claim size. For this last case, the optimal amount invested will not be bounded.