Optimal Reinsurance and Investment via Stochastic Projected Gradient Method Based on Malliavin Calculus

Abstract. This paper proposes a new approach for optimal reinsurance and investment strategies using the stochastic projected gradient method with Malliavin calculus. Unlike existing methodologies, we pursue static investment and reinsurance strategies by directly minimizing the ruin probability. In our setting, the ruin probability minimization problem is formulated as a nonconvex optimization problem over a convex set, and it is shown under suitable assumptions that the gradient of its objective function is Hölder continuous. Additionally, the theoretical guarantee of the proposed method is established by showing the convergence of the stochastic projected gradient method for general convex-constrained optimization problems whose objective function has Hölder continuous gradient. Numerical experiments demonstrate the benefit of directly minimizing the ruin probability.