Insurance design and tail risk management

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Modern insurance markets are facing more challenges than before due to changes in market conditions, and are calling for advanced concepts and novel methodologies to study sophisticated market participants' behaviours and to develop advanced risk management strategies. The proposed research focuses on establishing optimization problems to address concerns for insurance market participants, developing quantitative methodologies in risk management, and providing market participants scientific support on using insurance policies and risk measures to efficiently manage risks. This research will address two theme areas: (A) Analysis of insurance supply and demand. In insurance markets, participants use (re)insurance policies to effectively optimize their personal perspectives. Current research mainly focuses on optimization problems for individual policies, while provides limited discussion at the market level, in which complicated interplay among participants or risks challenges the existing methodologies. We aim at using three sets of advanced mathematical and economic tools to establish and to solve optimization problems at the market level. We will analyze insurance demand and supply for the entire market, and reveal the possible mismatch. Precisely, we will bring the behaviour theory in the formulation of nonperfect rationalities for participants due to the limitation on acquiring information, use game theory to describe the negotiation of the insurance policies among participants with different sets of information, and introduce systematic risk to characterize and to control the dependence among risks. (B) Tail risk management. In banking and insurance regulations, measuring tail behaviour of risks has become a standard assessment for risks and regulatory capital calculation. Classical insurance theories rely on the diversification and the risk pooling effect. However, modern markets and participants therein have become more vulnerable due to the occurrence of large-scale loss events and the dependence among risks, especially in the tails. Therefore, it is necessary to quantify risk behaviours in the tail and further develop effective risk mitigation strategies. To this end, we will further extend the study of tail risk measures and their applications, characterize tail dependence for a portfolio of risks, and investigate the effectiveness of (re)insurance in an insurer's tail risk management. Technique on risk sharing and properties of risk measures will be used to study bounds on essential quantities of the aggregate risks. Impact. Canada has internationally leading research in actuarial science. The proposed research helps to understand existing challenges in Canadian insurance markets better and to gain innovative techniques on overcoming those problems. Graduate students can obtain sufficient training through this research program to support their future career in both academia and insurance industry.