Hi Could someone help to answer the following questions please? What does "long-tail" mean? Sometimes the notes refer to low frequency and high severity claims while other places say long tail means a class of insurance where claims may take many years to emerge after the cover has ended like employer liability insurance. They are actually quite different. "Pension fund may not be allowed by scheme rules or regulation to hold some hypothetical assets" - please explain this sentence and provide some examples How to choose the threshold u used in GPD in modelling extreme events by using mean excess function? If we look at the the graph on the IAA notes (Plot e(u) against u, e(u) initially falls significantly and after a certain point it begins to increase, does that mean this certain point is the threshold u?? COSO cube says business level has subsidiary, business units, divisions and entity. I am sure about the hierarchy and could anyone provide an example in the context of a financial conglomerate? Thanks very much for your help
Hi Martina, Those are some really good questions and it did get me thinking. So here is my stab at answering them, but I do appreciate that my knowledge is limited and it may need verification by more knowledgeable students / tutors: I'd think of low frequency / high impact events as those arising from "fat / heavy tailed" distributions as opposed to being "long tailed". I do get the point that most fat tailed distributions will look long tailed as they have extreme values but the "length" there is in respect of the range / volatility of values. Insurance claims which take time to emerge are described as "long tailed" in the sense of "time" as it takes a long time emerge / fully crystallise (but the values may still be small / as expected). So even if we were to look at both the low frequency / high impact events and insurance claims as being described as "long tailed", the former will be a long tail in terms of values of the distribution while the latter is more likely to be long tailed in terms of the time it takes to emerge. I think this is referring to some cool assets like complex derivatives which may be prevented by the scheme rules. They are potentially hypothetical if such an instrument are not available / easily obtainable in the market. So at a high level, I'd think of any instrument which requires high level of financial engineering / bespoke structuring as "hypothetical" in the pension scheme's eyes. My understanding here is that you'd plot e(u) against u and pick u to be the smallest value above which e(u) becomes linear in u. I'd say we will not worry too much about what happens to e(u) before it gets to the point where it starts becoming linear. If we think of a financial conglomerate which has both Banking and Insurance activities, my guess of it structure would be as follows: Entity - the parent Group Subsidiary - Insurance sub and Banking sub BU - Life and General BUs within the Insurance sub, Retail and Investment Banking BUs within the Banking sub Divisions - Underwriting div + Pricing div within the Life and General insurance BUs, Deposit div+ Credit div etc within the Retail Banking BU, Trading div + Advisory div etc with the Investment Banking BU etc. I hope this helps (or atleast not confuse you more).
Fantastic answer, thank you Nirru. 1. I think the use of the phrase 'long-tailed' can have two meanings. Hopefully the context of the question will clear up which one is required. If you are trying to fit a distribution to some claims data, then long-tailed may mean that there are a small number of very high claim amounts, ie the tail of the PDF stretches out a long way. This is the CT6 (CS2) interpretation. However, if we refer to a 'long-tailed' class of business, then this generally means that the claims take a long time to be reported and settled, eg liability insurance. As such, the insurer would seek longer-term assets to match these liabilities. 2. This one is tricky without the context - do you remember where you saw this phrase? I'm wondering if it may hark back to times gone by when pension funds were able to value their assets based on a 'notional' portfolio, eg a portfolio that was assumed to match the liabilities. 3. Agree with Nirru. You are looking for the graph of e(u) vs u to become linear. This is because the theoretical mean of the excess X-U|X>U is a linear function of the mean E[X-U|X>U]. Eg if X is Pareto(a, b) then X-U|X>U is Pareto(a, b+U) and the mean of this distribution is (b+U)/(a - 1), which is linear in U. Eg if X is Exp(a) then X-U|X>U is Exp(a) by the memoryless property and the mean of this distribution is 1/a, which is just a constant. e(u) is the sample equivalent of E[X-U|X>U] so we are looking for the point where the graph of e(u) becomes linear. This normally occurs after the initial significant fall. 4. Great examples from Nirru. Another example is BPP: Entity is Apollo Education Group Ltd (the parent company). A subsidiary is BPP Holding Ltd (a subsidiary is a separate legal entity that must be at least 50% owned by the parent company). Divisions are BPP University, BPP Accountancy and Tax, BPP Actuarial Education, BPP Financial Services, BPP Professional Apprenticeships, BPP Professional Development, BPP Learning Media Business units might be HR, finance, legal, operations, IT, tutoring ... Some of the distinctions get a bit blurred, for example, some of the divisions I list above are also subsidiaries, eg BPP University Ltd, BPP Actuarial Education Ltd are subsidiaries of BPP Holdings. Also ActEd is a subsidiary of BPP Actuarial Education Ltd. The key thing to take away from this is that ERM should apply at all levels of an enterprise from highest to lowest. Good luck for the exam! Anna
