Decision making under uncertainty with an application to wildfire risk

Expected utility (EU) theory suggests that individuals make choices among risky outcomes by choosing the outcome that maximizes their well-being. The theory posits that choices are compared by calculating the expected utility of each choice, which is the product of the probability that a risky event will occur and the utility of the event if it does occur. It is usually assumed that individuals are risk averse which implies a concave utility function for wealth: a sure outcome V is preferred over any gamble with an expected outcome of V. This form of the utility function gives rise to the rationale for voluntarily purchasing insurance to protect against natural hazards. EU theory predicts that, when faced with the prospect of encountering natural hazards that decrease personal wealth, people will purchase insurance to protect their assets. However, there is ample experimental and field evidence in the natural hazard literature that EU theory is often violated. The inability to correctly assess the risk from very low probability events and the convexity of the utility function over losses have been offered as explanations. Further, catastrophic hazards may not conform to Gaussian probability theory, confounding risk assessments in a world that is perceived as “normal” by those facing natural hazards. We review the economic implications of these explanations and present an application of extreme value statistics using wildfire data. The distribution of wildfire size is estimated using the Generalized Pareto Points Over Threshold (POT) model. We include weather data as a covariate in calculating the scale parameter of the model to show how the fire size distribution shifts with changes in weather.