Portfolio Selection as introduced by Harry Markowitz laid the foundation for Modern Portfolio Theory. However, the assumption that underlying asset returns follow a Normal Distribution and that investors are indifferent to skew and kurtosis is not practically suited for the Hedge Fund environment. Additionally, the Lockup and Notice provisions built into Hedge Fund contracts make portfolio rebalancing difficult and justify the need for dynamic allocation strategies. Market conditions are dynamic, therefore, rebalancing constraints in the face of changing market environments can have a severe impact on return generation. There is a need for sophisticated yet tractable solutions to the multi-period problem of Hedge Fund portfolio construction and rebalancing. In this thesis we Generalize the Hedge Fund asset return distribution to a Multivariate K-mean Gaussian Mixture Distribution; model the multi-period Hedge Fund allocation problem as a Markov Decision Process (MDP); and propose practical rebalancing strategies that represent a convergence of literature on Hedge Fund investing, Regime Switching, and Dynamic Portfolio Optimization.