Beyond the Ruin Problem: Novel applications of Insurance Risk Models

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The proposed research program seeks to contribute to the field of insurance and financial mathematics in two fronts. A first component will focus on extending the current state of knowledge in insurance risk theory, in particular in ruin theory and risk measures. However, the direction of such generalizations will be mainly dictated by the modeling needs of practical applications. Indeed, the second component of our research program will build upon the exploration of practical applications of the mathematical and statistical technology developed in the field of insurance risk theory and in particular ruin theory and casualty insurance modeling. ***There is a large body of knowledge that has been constructed over several decades and we now have good theoretical frameworks in several areas of insurance modeling. Over the next five years, I propose to explore applications in other fields under the lens of the understanding and framework provided by insurance risk theory. Indeed, advances in insurance risk theory and casualty insurance involve tools and concepts from different fields such as stochastic analysis, statistical inference, theory and estimation of stochastic processes. There are areas in finance and insurance where the building blocks from classical insurance risk theory, as well as the processes and methods themselves, arise naturally. The main fields where we intend to explore applications are, but not limited to, market micro-structure and credit risk. Indeed, more complex models describing the different degrees of complexity behind these two applications need to be studied. These needs intersect nicely with the body of knowledge in insurance risk theory and applications arise naturally and are the subject of the proposed research program. This research program seeks to explore theoretical questions around the so-called insurance risk processes and the ruin problem in directions that determined not by what is technically possible and a logical next step from a theoretical standpoint but they are dictated by applications.