Sooie-Hoe Loke's Abstract
A natural measure of risk in the insurance business is the probability of ruin, which is the probability that the insurer's surplus level eventually falls below zero. Depending on the nature of the business, there are various ways to model its surplus process. In this talk, we will revisit the well-known Cramer-Lundberg model and discuss some properties regarding its corresponding ruin probability including exact expression, asymptotic behavior, convexity, etc. We will then look into the ruin probabilities in other models including the dual risk model and multidimensional risk model. Recent developments and themes in ruin theory such as reinsurance, capital injection, risky investment, and incurred but not reported (IBNR) claims will also be discussed.