Analysis of first passage times with risk management applications

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The financial crisis of 2007-2008 (also known as the Great Recession) has had extensive impact on the practice of risk management in insurance and finance. The importance of designing and implementing good risk management practices was painfully demonstrated in some cases and shown to be a determining factor in an insurer's ability to weather the last period of extreme financial instability. Insurers and other important financial players have since increased their risk management activities by most notably characterizing new and emerging threats, quantitatively assessing these threats, and developing cutting-edge techniques to mitigate potential risks via the use of the most up-to-date financial instruments, modern design of insurance policies, as well as other means. Also, the insurance industry has since heavily invested on the development of a more sophisticated and integrated risk management framework to better assess an insurer's solvency risk. My proposed research program is expected to make significant contributions in this immediate field of research. The development and the subsequent analysis of general insurance risk models are a central theme of my research.***More specifically, my proposed research pertains to the analysis of an insurer's cash flow dynamics with a special focus on the risks inherent to periods of financial stress. Central to my research program are stress periods which begin either with a capital shortfall episode (ruin) or extreme negative shocks in capital levels (drawdown). Building on the recent trend in the scientific community, risk measures with additional path-dependent features will be introduced and further analyzed to assist in the early detection of potential risks. My research will lead to significant advances in mathematical theory and related techniques for the study of risk processes. Related disciplines in applied probability (such as queueing theory and fluid flow theory) will also benefit from such advances. This will solidify the transfer of knowledge among these research disciplines. Another main objective of my proposed research consists in the development of risk models which will subsequently allow for a quantitative measurement of the benefits of proper risk management practices. Both analytic and probabilistic techniques are expected to be used to conduct the alluded analysis.**