Quantitative methods for risk management

他们做这些假设是为了做他们花哨的数学！这是我们所有学术精算师都从从业者那里听到的指控，不管这些从业者多么精通数学。就在几天前，斯蒂芬理查兹，一个执业精算师（FFA）和博士。在风险与保险研究中心/舒里奇商学院的一次联合学术讨论会上，他以尖刻的方式批评了数学中的“与现实零联系的花哨数学模型”。无论斯蒂芬的话是否属实，作为负责任的学者，我们必须意识到这一相当普遍的观点，它加剧了象牙塔和工作场所现实之间已经存在的巨大差距。这个建议是一个努力提出深入的数学方法，解决这些问题所带来的实践风险专业人员。 三个不同的，但连接的研究线程，这是风险聚合，风险分配和可变性评估，在这个建议中，通过一个可疑的风险从业者的透镜进行了批判性的探讨。具体来说，我们解决了一些不方便但突出的问题，都是这样的：“如果假设XYZ是不合适的呢？”，其中各种XYZ是由加拿大保险公司和银行的精算师和定量风险专业人员确定的。简单地说：在第一节中，我们提出了一个有效的算法，该算法能够快速而准确地近似具有不同参数族分布的相关风险和的分布，而不考虑被求和项的数量和所涉及的重尾性;在第2节中，我们主张如何对待风险资本配置的范式转变，作为一种副产品，统一了自上而下和自下而上的风险资本配置方法;在第3节中，我们阐明了测量leu方差变异性的途径，特别是，我们建议发展著名的Hattendorff定理的重尾变化，该定理分配可变性--当用连贯的和共单调的可变性加性度量来测量时--未来几年几乎任何付款流和规则的积累利息。 将从拟议的研究中产生的方法论是真正的行业驱动的，因此具有直接的翻译重要性，以及严格和最高的学术水平。套用史蒂夫·乔布斯的话，我可以真诚地说，正是美丽的数学与社会公益的结合让我的心歌唱。我真的很高兴有能力的翻译研究，其中这个建议是一个例子。

``They are making those assumptions in order to do their fancy maths!'' is an accusation that all of us, academic actuaries, have heard from practitioners, irrespective of how mathematically savvy these practitioners are. Just a few days ago, Stephen Richards, a practicing actuary (FFA) and a Ph.D. in Mathematics criticized in an acerbic manner ``fancy mathematical models that have zero connection with reality'' at a joint Risk and Insurance Studies Centre / Schulich School of Business colloquium talk. Whether or not there is some truth to Stephen's words, as responsible academic we have to be aware of this rather common opinion, which aggravates the already profound gap between the ivory tower and the workplace reality. This proposal is an effort to put forward deep mathematical methods, which solve those problems that are brought up by practicing risk professionals. Three distinct and yet connected research threads, which are risk aggregation, risk allocation and variability assessment, are explored in this proposal critically through the lens of a dubious risk practitioner. Specifically, we address somewhat inconvenient but salient questions that all go like this: “What if assumption XYZ is inappropriate?”, where the various XYZs were identified by a number of actuaries and quantitative risk professionals in Canadian insurance companies and banks. Speaking briefly: In Section 1, we put forward an efficient algorithm, which is able to approximate - fast and accurately irrespective of the number of summands and involved heavy-tailedness - the distributions of sums of dependent risks having distributions in distinct parametric families; In Section 2, we argue for a paradigm shift as to how risk capital allocations should be treated and, as a by product, we unify the top-down and the bottom-up approaches to allocate risk capital; In Section 3, we shed light on the routes to measure variability in leu of variance, and in particular, we propose to develop heavy-tailed variations of the celebrated Hattendorff's theorem that allocate the variability - when measured by coherent and comonotonically additive measures of variability - to future years for virtually any payment stream and rule for accumulation of interest. The methodologies that will be coming out of the proposed research are truly industry-driven and so of direct translational importance, as well as rigorous and of the highest academic caliber. Paraphrasing Steve Jobs, I can genuinely say that it is beautiful mathematics married with social good that makes my heart sing. I am really thrilled about the capable translational research, of which this proposal is an example.