An optimal investment strategy with maximal risk aversion and its ruin probability in the presence of stochastic volatility on investments

•A verification theorem which relates the value function with the HJB equation.•Existence and uniqueness theorem and an explicit form of the optimal strategy of investment.•Numerical simulation of the expected utility.•An upper bound for the ruin probability.

In this paper, we study an optimal investment problem of an insurance company with a Cramér-Lundberg risk process and investments portfolio consisting of a risky asset with stochastic volatility and a money market. The asset prices are affected by a correlated economic factor, modeled as diffusion process. We prove a verification theorem, in order to show that any solution to the Hamilton-Jacobi-Bellman equation solves the optimization problem. When the insurer preferences are exponential, we prove the existence of a smooth solution, and we give an explicit form of the optimal strategy, also numerical results are presented in the case of the Scott model. Finally we use the optimal strategy to get an estimate of the ruin probability in finite horizon.