Measures and Models for Dependent Actuarial Risks

我的研究方向是精算学中的风险管理。投资组合管理的一个主要缺点是对风险缓解的系统考虑。由于监管或会计规则的原因，投资组合的所有风险并不总是可以汇总的。此外，即使它们可能是，为了进行风险比较，或者为了更准确和保守的保护，可能需要单独考虑它们或将它们放在同类组中。在我的五年研究计划中，我将通过多变量框架来研究这个问题。后者最近被引入精算学领域，用于风险计量。它越来越受欢迎，无论是在加拿大的学者和从业人员，并在大多数发达国家。* 我计划开发封闭形式的表达式并研究多变量风险度量的属性。一个新的多变量风险度量，多变量截断尾风险值（mTTVaR）将被开发，以衡量在一个特定的封闭范围内的概率损失。将重新研究基于多变量数据的自然风险统计，因为基于总风险的夫妇排序限制了其使用。我将研究不同的排序，以提供更易处理、更稳健、更可靠和更实用的统计数据。我将开发多变量置信区域的估计量，并将其与多变量接受集进行比较。我们将区分具有非常相似定义的实际多变量风险度量，除了考虑多变量集的方式不同，提供不同的统计数据。我还打算提供封闭形式的表达式，多变量风险措施与常见的多变量随机过程和分布在精算科学。将开发和研究基于多变量尾风险值和mTTVaR的精算模型适用性的统计检验。**我的计划的第二部分是致力于多变量风险措施的应用。我将从金融和精算的角度研究使用多变量风险度量对保险、再保险和金融产品定价的影响。我将研究一些特殊的原则，以优化联合互惠再保险合同，例如，当配额份额和调整因子同时设置。优化将基于联合生存和盈利能力分布。最后，我们将结果推广到一个多元再保险合同。从相关风险的投资组合的同质类别中保护风险对于几个目的是有用的。它允许为每个风险分配价值，比较它们，评估每个业务线，并为风险管理目的或偿付能力要求分配资本。挑战是创新和原创的。他们将为研究生，学者和学者提供有趣的研究项目。

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.