Per 1 January 2016 the new supervision framework Solvency II will be implemented for insurance companies. In this paper we want to investigate the optimal investment strategy for an insurance company under the new Solvency II framework. We can formulate this as an optimization problem where the expected surplus is maximized subject to several constraints: a budget constraint and various “risk constraints” meaning that the Solvency Capital Requirements (SCR) the company needs to hold for an asset portfolio cannot exceed a certain fraction of the initial surplus.