This article draws on stylized facts to build a dynamic portfolio allocation model of sovereign wealth funds (SWF). We show that a traditional dynamic Merton allocation model allows for the stylized evidence that, on the one hand, the shares of monetary assets in such funds grow with the risk aversion of the state-investor in time, and on the other hand, these funds include the presence or absence of hedge funds correlated to the financial situation. One weakness of this model is its prediction of a lower risk/riskier asset ratio for sovereign stabilization funds and generational savings sovereign funds. This result contradicts the stylized fact of a lower risk/riskier asset ratio in stabilization funds than in generational savings funds. A dynamic model inspired by the theoretical framework of Bajeux-Besnainou et al. [1] is compatible with all the stylized facts.