This work addresses the limitations of the expected utility theory in predicting risk preference under low probabilities. This topic has particularly not been addressed before when ambiguity is coupled with low probability estimates. The reader will find a theoretical analysis of ambiguity aversion when individuals purchase insurance for low-probability loss events. The topic has been looked into under the light of forest carbon offsets and the need for insurance for unavoidable losses of the sequestrated carbon. That is because wildfire losses have small probabilities of occurrence and are associated with ambiguity. The growing importance of using biological sinks toward emissions reduction only heighten the significance of this topic. The book also offers an experimental design involving three phases, including a replica of a previous study on insurance behaviour, the addition of the ambiguity factor, and two methods of measuring ambiguity preference. This book is particularly useful for experimental and environmental economists, and anyone interested in government policies pertaining carbon offsets.