Risk measures in portfolio selection and optimal reinsurance

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Risk and uncertainty are the indispensable nature of the financial and insurance markets. Financial mathematicians and actuaries use risk measures to quantify the risk. The risk measures we use have evolved from qualitative descriptions to a more quantitatively measuring of risk. Abundant research has been carried out to study the statistical property of various risk measures but little is known about how these risk measures can affect risk management decisions in financial and insurance institutions. The proposed research program intends to investigate the use of various risk measures in portfolio selection with behavioral considerations. The existing literature focuses on only a few classical risk measures with no attention paid to alternative risk measures especially those introduced recently. Moreover, the existing work assumes the decision-maker is rational and risk-averse, which is challenged by the theory of behavioral finance that there are systematic anomalies in human behavior that are incompatible with rationality. We plan to consider optimal investment decisions in the presence of risk constraints in which the risk is measured by various risk measures. We will allow the decision-maker to have behavioral preferences to account for human emotions and psychology. We shall also examine how various risk measures can affect financial market stability. Apart from portfolio selection, we plan to study the design of optimal reinsurance which is the most common tool for insurance companies to manage their risk exposures. The existing literature focuses on relatively simple premium principles and the optimal reinsurance strategy is typically restricted to either proportional reinsurance or excess-of-loss. The research program will consider reinsurance strategies among a general class of contracts when the reinsurance premium is calculated according to various risk measures. These are challenging problems, as only similar problems for very special cases have been studied in the literature with ad hoc methods. We will make use of the existing optimization and stochastic control techniques and develop new methods to solve the problems. This might be one of the first few attempts to systematically analyze the impacts of various risk measures on risk management decisions taking into consideration human psychology. We expect the findings of the research program will help financial managers, insurers, and regulators have a better understanding of various risk measures. In particular, the results will provide new guidance on risk management for Canadian and global financial and insurance markets. By establishing and analyzing new mathematical models, the research will contribute to optimization techniques that will be useful to other problems in mathematical finance and actuarial science. HQPs involved will develop skills in quantitative risk management necessary for a career in the financial and insurance industry, as well as in academia.