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{{Redirect-synonym|TVAR|[[Time variance]]}}
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'''Tail value at risk''' ('''TVaR'''), also known as '''tail conditional expectation''' ('''TCE''') or '''conditional tail expectation''' ('''CTE'''), is a [[risk measure]] associated with the more general [[value at risk]]. It quantifies the expected value of the loss given that an event outside a given probability level has occurred.
 
==Background==
 
There are a number of related, but subtly different, formulations for TVaR in the literature. A common case in literature is to define TVaR and [[average value at risk]] as the same measure.<ref name=Bar/>  Under some formulations, it is only equivalent to [[expected shortfall]] when the underlying [[cumulative distribution function|distribution function]] is [[continuous function|continuous]] at <math>\operatorname{VaR}_{\alpha}(X)</math>, the value at risk of level <math>\alpha</math>.<ref name=web1/> Under some other settings, TVaR is the conditional expectation of loss above a given value, whereas the expected shortfall is the product of this value with the probability of it occurring.<ref name = "Sweeting"/> The former definition may not be a [[coherent risk measure]] in general, however it is coherent if the underlying distribution is continuous.<ref name=Acerbi/> The latter definition is a coherent risk measure.<ref name = "Sweeting" /> TVaR accounts for the severity of the failure, not only the chance of failure. The TVaR is a measure of the [[Expected value|expectation]] only in the tail of the distribution.
 
==Mathematical definition==
 
Given a [[random variable]] <math>X</math> which is the payoff of a portfolio at some future time and given a parameter <math>0 < \alpha < 1</math> then the tail value at risk is defined by<ref name=Artzner/><ref name=Landsman/><ref name=Landsman2/><ref name=Valdez/>
: <math>\operatorname{TVaR}_{\alpha}(X) = \operatorname{E} [-X|X \leq -\operatorname{VaR}_{\alpha}(X)] =  \operatorname{E} [-X | X \leq x^{\alpha}] ,</math>
 
where <math>x^{\alpha}</math> is the upper <math>\alpha</math>-[[quantile]] given by <math>x^{\alpha} = \inf\{x \in \mathbb{R}: \Pr(X \leq x) > \alpha\}</math>. Typically the payoff random variable <math>X</math> is in some [[Lp space|L<sup>p</sup>-space]] where <math>p \geq 1</math> to guarantee the existence of the expectation.
 
==References==
{{Reflist|refs=
 
<ref name=Bar>{{cite journal|last=Bargès|coauthors=Cossette, Marceau|title=TVaR-based capital allocation with copulas|journal=Insurance: Mathematics and Economics|year=2009|volume=45|pages=348–361|url=http://www.sciencedirect.com/science/article/pii/S0167668709000912|accessdate=20 July 2012|doi=10.1016/j.insmatheco.2009.08.002}}</ref>
 
<ref name=web1>{{cite web|url=https://statistik.ets.kit.edu/download/doc_secure1/7_StochModels.pdf|title=Average Value at Risk|format=pdf|accessdate=February 2, 2011}}</ref>
 
<ref name = "Sweeting">{{cite book
| last          = Sweeting
| first         = Paul
| title        = Financial Enterprise Risk Management
| series        = International Series on Actuarial Science
| year          = 2011
| publisher    = [[Cambridge University Press]]
| isbn          = 978-0-521-11164-5
| lccn          = 2011025050
| pages        = 397–401
| chapter      = 15.4 Risk Measures
}}</ref>
 
<ref name=Acerbi>{{cite journal|first1=Carlo|last1=Acerbi|first2=Dirk|last2= Tasche|title=On the coherence of Expected Shortfall|year=2002|journal=Journal of Banking and Finance|volume=26|number=7|pages=1487–1503|url=http://arxiv.org/pdf/cond-mat/0104295%22%20/|format=pdf|accessdate=April 25, 2012}}</ref>
 
<ref name=Artzner>{{cite journal|last=Artzner|first=Philippe|last2=Delbaen|first2=Freddy|last3=Eber|first3=Jean-Marc|last4=Heath|first4=David|year=1999|title=Coherent Measures of Risk|journal=Mathematical Finance|volume=9|issue=3|pages=203–228|url=http://www.math.ethz.ch/~delbaen/ftp/preprints/CoherentMF.pdf|format=pdf|accessdate=February 3, 2011}}</ref>
<ref name=Landsman>{{cite journal|first1=Zinoviy|last1=Landsman|first2=Emiliano|last2=Valdez|title=Tail Conditional Expectations for Exponential Dispersion Models|date=February 2004|url=http://www.actuaries.org/ASTIN/Colloquia/Bergen/Landsman_Valdez.pdf|format=pdf|accessdate=February 3, 2011}}</ref>
<ref name=Landsman2>{{cite journal|first1=Zinoviy|last1=Landsman|first2=Udi|last2=Makov|first3=Tomer|last3=Shushi|title=Tail Conditional Expectations for Generalized Skew - Elliptical distributions |date=July 2013|url=http://papers.ssrn.com/sol3/papers.cfm?abstract_id=2298265|format=pdf|accessdate=June 30, 2013}}</ref>
<ref name=Valdez>{{cite journal|first=Emiliano|last=Valdez|title=The Iterated Tail Conditional Expectation for the Log-Elliptical Loss Process|date=May 2004|url=http://www.asb.unsw.edu.au/schools/actuarialstudies/Documents/E.A.%20Valdez%20-%20The%20Iterated%20Tail%20Conditional%20Expectation%20for%20the%20Log-Elliptical%20Loss%20Process.pdf|format=pdf|accessdate=February 3, 2010}}</ref>
}}
 
{{DEFAULTSORT:Tail Value At Risk}}
[[Category:Actuarial science]]
[[Category:Mathematical finance]]
[[Category:Financial risk]]
 
 
{{Econometrics-stub}}
{{Finance-stub}}

Latest revision as of 07:28, 9 December 2014

Have you recently become into some legal problems? Perhaps you are the sufferer of a criminal offense? Perhaps you only want to setup a full time income have confidence in. What ever your factors, you will want a good lawyer. Unfortunately, choosing a good attorney can be quite a tad difficult. Look at the adhering to report for several crucial tips that will help you atlanta car accident lawyer (http://www.youtube.com/) engage a very good attorney.

If you notice the legal professional you chose is not really carrying out work that you had been anticipating, do not hesitate to flame them. This is actually the particular person you are having to pay your money for, so at any point you can reduce ties. If you are experiencing a legal issue, you merely want the ideal in your corner.

You ought to concur with exactly how much you will spend your legal professional prior to getting them. Request your legal professional for the quote right after explaining what exactly you need help with and sign an agreement. Do not be reluctant get in touch with diverse attorneys so that you can evaluate rates and judge a lawyer you can pay for.

Never ever be reluctant to ask your legal professional about any section of the fees you do not understand. There are lots of people who have complications with the costs they may be charged by legal counsel, but a lot of them will not say anything at all. There exists a chance that can be done a few of the operate yourself and save a little, so make sure to find out about that.

In choosing a legal professional, recommendations is among the guidelines on how to find one. Ask good friends or relatives for referrals. They can give you sincere feedback on the experience. They can tell you how good or badly they did inside their scenario. This opinions will help you pick wisely.

Never choose the initial legal professional you discover within the yellow pages. It's very crucial that you do some research about the matter initial. You can receive some poor unexpected situations in the event you basic your choice only with a professional recommendation from a friend or acquaintance. It will always be preferable to be secure than sorry.

Ask everybody you know if they've applied an attorney for the legal situation for example the one you have, and who they could suggest. Don't overlook to gather personal references for that legal representatives on the simple checklist and take a look. Also conduct a background check and Yahoo and google them to see what other individuals say with regards to their professional services.

Don't just opt for the first legal representative you find on the web. It can be appealing to think legal representatives all do the same thing, however they may differ in top quality and experience. Ask friends once they know a good lawyer and what he represented them for. Be fussy when choosing lawful aid.

Offer an substantial selection of queries for your probable attorneys. In an initial assessment, the legal representative should be prepared to respond to any concern that you may have, big or small. They should ensure your comfortable with their expertise. If you do not feel at ease, then you certainly need to find a person more to represent you.

Most legal professionals charge for solutions from the hour or so, but employing one by using a decrease hourly charges does not always mean your total cost will be significantly less. In case your attorney requires two hours to accomplish work that various other attorney can total within an 60 minutes, you may pay much more in the end.

With regards to selecting lawful reflection, you want to make certain that you are receiving the very best help within your budget. Currently, it really is much too an easy task to get stuck by using a lawyer who just isn't heading to provide all of their focus. Make use of the ideas offered on this page if you would like create your legal representative lookup more lucrative.

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