Over the last few decades, it has become increasingly important to study and solve problems of portfolio optimization. For the focus of this dissertation, we consider an optimal investment problem in which an investor allocates his or her wealth among cointegrated risky assets. We consider both power and logarithmic utility functions to describe the investor's risk aversion preferences. The investor seeks to find the optimal portfolio to maximize his or her expected utility from terminal wealth, given the dynamics of the cointegrated assets' prices and total wealth. We also study this optimization problem in the regime of fast mean-reversion for the cointegrated asset prices. We solve this continuous-time problem according to the typical Hamilton-Jacobi-Bellman Equation structure. We explicitly solve this particular problem by recognizing a correct guess solution for the optimal value function and ultimately end up solving a system of ODEs for which the explicit solution depends on. In addition, we resolve this optimization problem by a similar method to obtain an approximation solution for the value function. In the regime of fast mean-reversion, the impact of cointegration on this problem becomes particularly interesting for large enough mean-reversion rates. Under these conditions, we also find that the approximation solution becomes a better estimate for the true value function. In addition, here the investor can take adavantage of the market to make potentially enormous, even infinite, amounts of money through constantly rebalancing his or her portfolio. This seemingly ideal situation is unrealistic, and we thus must incorporate transaction costs into the model. With transaction costs added, this optimization problem involving cointegrated assets unfortunately does not admit an explicit solution. However, we can numerically analyze mutliple forms of this problem.