Optimal reinsurance designs and related problems

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My research interests lie in developing effective quantitative tools to evaluate and manage risks in problems related to insurance and finance. The primary objective of this research proposal is to develop theoretically sound and yet practical solutions in the quest for optimal reinsurance. My previous research program has obtained a series of interesting results by focusing on risk measure minimization reinsurance models, and by exploiting two important risk measures known as Value-at-Risk and Conditional Tail Expectation. This area of research is inspired by the prominent use of these two risk measures in risk management by banks and insurance companies, and by their important role in solvency regulation as adopted by various authorities. One of the long-lasting challenges with optimal reinsurance designs is the mathematical difficulty of solving the corresponding optimization problems. To circumvent this difficulty, I developed a new empirically-based approach for analyzing optimal reinsurance. This approach formulates the reinsurance models directly based on empirical data, and it allows us to address the optimal reinsurance designs for a wide class of models. While fruitful research results have been achieved, there are still many important directions worth further exploration. Broadly, they can be categorized into three groups: (1) exploration of the statistical properties of the empirical approach; (2) application of the empirically-based approach to more reinsurance models; (3) generalizing the results achieved to other optimality criteria and other reinsurance premium principles. I also plan to conduct research on the topics of partial hedging and robust portfolio selection in finance, as they are closely related to the topic of optimal reinsurance designs. I strongly believe that the research I am proposing will be of significant interest to both academicians and practitioners.