Asymptotically Optimal Investment for Risk Model with Random Income and Diffusions

In this paper, an insurer with perturbed classical risk process and random premium income has the possibility of investment into a risky market. The price process of the risky market is assumed to follow a geometric Brownian motion. The aim of this paper is to obtain the asymptotical behavior of the ruin probability under the optimal strategy in the small claims. The constant (denoted by maximizing the Lundburg exponent is derived. It turns out that the optimal investment level convergence to when the initial surplus tends to infinity. That is to say, the constant we found is the asymptotically optimal strategy