Minimization of absolute ruin probability under negative correlation assumption

In this paper we consider the problem of minimizing the absolute ruin probability of an insurance company. The managers of the company control investment amount and risk exposure to minimize the absolute ruin probability. A negative correlation between insurer's liabilities and capital gains in financial market is introduced. Under this negative correlation assumption, the explicit forms of the solutions and optimal strategies to this problem for all different parameters are derived. We find that the solutions of this problem are S-shaped and the optimal strategies fail to be monotonic or continuous.