In the first essay, we prove existence and uniqueness of equilibrium in a rent-seeking contest given a class of heterogeneous risk-loving players. We explore the role third-order risk attitude plays in equilibrium and find that imprudence is sufficient for risk lovers to increase rent-seeking investment above the risk-neutral outcome. Moreover, we show that rent can be fully dissipated in a standard Tullock contest when there is a large number of risk-loving players. In the second essay, we investigates the impact classic variables like medical care and lifestyle choices have on the mean, variance and skewness of a health distribution. We achieve this by positing health as output from a stochastic production process, a seemingly practical advantage over much of the deterministic literature. We leverage this unique approach to estimate how a set of explanatory variables impact the conditional moments of a health distribution. We then use these moments in a maximum entropy framework to analyze the shape impact of medical care. We find evidence of ``flat of the curve'' medicine but also demonstrate the higher-order benefits of additional medical care. In the third and final essay, we investigate risk in the context of farmer and their choice of irrigation. While the benefits and utilization of crop irrigation have long been examined in agricultural economics, little attention is paid to the potential confounding relationship that may exist with other risk-management tools. Specifically, we pursue how standard crop insurance relates to irrigation. We identify irrigation as a form of self-protection, reducing the probability of crop loss due to adverse stochastic conditions. Given this, we investigate if irrigation acts as a complement to crop insurance. We test this relationship within a model of crop yields, identifying that jointly irrigated and insured lands both receive higher average yield and lead to variance and skewness effects on the overall yield distribution.