Decision making problems in Actuarial Science

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In 2017, global insured losses from catastrophe (CAT) events were USD 144 billion (swiss Re), the highest-ever recorded in a single year. In Canada, the figure was about $1.33 billion (CatIQ). These losses cause serious capital shortage or even solvency problems for insurance companies. Therefore, it is extremely important for insurance companies to hedge these risks. Without proper hedging arrangements, insurance companies may become insolvent, the public exposed risks may not have their claims paid, or the government agencies may need to bail out one or more insurers at the ultimate expenses of the tax payers. The goal of this research program is to study the optimal approach to integrate the available hedging mechanisms to build an effective catastrophe risk management system that considers the interests of all stakeholders, including insureds, insurance companies, reinsurance companies, investors, and the government. Insurers' two commonly used mechanisms to hedge CAT risks are (1) purchasing conventional reinsurance coverages from reinsurers, where the indemnity is a function of the primary insurer's covered losses; and (2) purchasing catastrophe loss index securities from the financial market, where the indemnity is a function of certain CAT loss index, such as industry-wide losses. The question to ask is how to make best uses of such mechanisms. The optimal reinsurance problem is an old one. There are deep results in the literature about what kind of reinsurance coverages insurance companies should purchase and how much it should spend on such coverages. Famous economists such as K. Borch and K. J. Arrow argued that to minimize an insurer's risks, measured by variance, or to maximize its expected utility, the optimal reinsurance policy should have a stop-loss form, where the portion of losses above certain threshold is paid by the reinsurance company. The research area is still very active, with current focus on the format of optimal reinsurance when risks are measured by more modern solvency related risk measures such as Value at Risk (VaR) and Tail Value at Risk (TVaR). There are much fewer results on optimal contracts for CAT loss index-based securities in the literature. However, active researches are being performed around the world. A key insight is that researchers have been studying the optimal reinsurance contracts or index-based securities separately. It is likely much more effective to integrate these  different hedging mechanisms to build a risk management system. Thus, studying the optimal approach to do so is the goal of this research program. To reach the goal, we will combine classical decision-making theory with advanced engineering models of natural hazards, such as earthquakes, in Canada. This combination was made possible by our close collaborations with Western's Civil Engineering team. We believe that this research program will contribute to building an effective Canadian CAT risk management system.