Investment and reinsurance strategies via minimizing Gerber–Shiu-like penalty function

This paper proposes a method for minimizing a Gerber–Shiu-like penalty function using a mini-batch stochastic projected gradient method (MBSPG) to determine optimal investment and reinsurance strategies. The Gerber–Shiu-like penalty function considers both the probability of ruin and the magnitude of loss when ruin occurs. To apply the MBSPG, we derive an unbiased estimator of the gradient via Malliavin calculus and establish Hölder continuity of the gradient. Numerical experiments demonstrate the effectiveness of our proposed method.