Measures and Models for Dependent Actuarial Risks

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My proposed research lies in the area of risk management in actuarial science. A major drawback of portfolio management is the systematic consideration of risk mitigation. All risks of a portfolio cannot always be aggregated, because of regulation or accounting rules. Moreover, even if they can be, it might be desirable to consider them individually or in homogeneous groups, for risk comparison, or for more accurate and conservative protections. In my five-year research program, I will investigate this issue through a multivariate framework. The latter has recently been introduced in the actuarial science field for risk measurement. It is gaining popularity, both with academics and practitioners in Canada, and across most developed countries. I plan on developing closed-form expressions and studying properties of multivariate risk measures. A new multivariate risk measure, multivariate Truncated Tail Value-at-Risk (mTTVaR) will be developed, to measure losses in a particular closed range of probabilities. Multivariate data-based natural risk statistics will be reinvestigated, since couple ordering based on aggregate risks restricts its use. I will study different ordrings to provide statistics that are more tractable, robust, reliable and practical. I will develop estimators for multivariate confidence regions and compare them with multivariate acceptance sets. We will distinguish actual multivariate risk measures that have very similar definitions, exept for differences in the way multivariate sets are being considered, providing different statistics. I also intend provide closed-form expressions of multivariate risk measures with common multivariate stochastic processes and distributions in actuarial science. A statistical test for the suitability of actuarial models, based on multivariate Tail Value-at-Risk and mTTVaR will be developed and studied.A second part of my program is dedicated to the application of multivariate risk measures. I will study the impact of using multivariate risk measures on the pricing of insurance, reinsurance and financial products, based on financial and actuarial points of view. I will investigate some particular principles, to optimize joint reciprocal reinsurance contracts, e.g. when both the quota-share and adjustment factors are set simultaneously. The optimization will be based on the joint survival and profitability distributions. Finally, we will extend the results for a multivariate reinsurance contract. Protecting risks from homogeneous classes of portfolios of dependent risks is useful for several purposes. It allows to allocate values to each risk, to compare them, to evaluate each business line and to allocate capital for risk management purposes or solvency requirements.The challenges are innovative and original. They will provide interesting research projects for graduate students, academics and practitionners.