The first essay addresses how investors price risk in the stock market when they cannot observe the true long-run growth rate of their consumption and dividend endowments. The model presents a number of import insights into how the ability of long-run risks to explain the equity risk premium is directly related to the quality of investors information sets. The second essay addresses the welfare costs of ambiguity surrounding the probability distribution of shocks driving the growth rate of their consumption endowment. If an investor faces both long-run risk and rare disasters in their consumption edowment, then they would forgoe a large share of their lifetime consumption to absolve ambiguity surrounding disasters, but substantially less to remove ambiguity about long-run risk. The third essay presents a dynamic stochastic general equilibrium model of a small open economy (SOE) that faces time-varying volatility of news about their total factor productivity and real interest rate. News uncertainty shocks about the interest rate motivate the SOE to deleverage, however, the same class of shocks in total factor productivity have insubstantial effects.