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Latest revision as of 04:56, 21 March 2013

In financial mathematics, a deviation risk measure is a function to quantify financial risk (and not necessarily downside risk) in a different method than a general risk measure. Deviation risk measures generalize the concept of standard deviation.

Mathematical definition

A function $D : ℒ^{2} \to [0, + \infty]$ , where $ℒ^{2}$ is the L2 space of random portfolio returns, is a deviation risk measure if

Shift-invariant: $D (X + r) = D (X)$ for any $r \in ℝ$
Normalization: $D (0) = 0$
Positively homogeneous: $D (λ X) = λ D (X)$ for any $X \in ℒ^{2}$ and $λ > 0$
Sublinearity: $D (X + Y) \leq D (X) + D (Y)$ for any $X, Y \in ℒ^{2}$
Positivity: $D (X) > 0$ for all nonconstant X, and $D (X) = 0$ for any constant X.^[1]^[2]

Relation to risk measure

There is a one-to-one relationship between a deviation risk measure D and an expectation-bounded risk measure R where for any $X \in ℒ^{2}$

R is expectation bounded if $R (X) > 𝔼 [- X]$ for any nonconstant X and $R (X) = 𝔼 [- X]$ for any constant X.

If $D (X) < 𝔼 [X] - e s s \inf X$ for every X (where $e s s \inf$ is the essential infimum), then there is a relationship between D and a coherent risk measure.^[1]

Examples

Template:Stub-section The standard deviation is clearly a deviation risk measure.

References

43 year old Petroleum Engineer Harry from Deep River, usually spends time with hobbies and interests like renting movies, property developers in singapore new condominium and vehicle racing. Constantly enjoys going to destinations like Camino Real de Tierra Adentro.

↑ ^1.0 ^1.1 One of the biggest reasons investing in a Singapore new launch is an effective things is as a result of it is doable to be lent massive quantities of money at very low interest rates that you should utilize to purchase it. Then, if property values continue to go up, then you'll get a really high return on funding (ROI). Simply make sure you purchase one of the higher properties, reminiscent of the ones at Fernvale the Riverbank or any Singapore landed property Get Earnings by means of Renting

In its statement, the singapore property listing - website link, government claimed that the majority citizens buying their first residence won't be hurt by the new measures. Some concessions can even be prolonged to chose teams of consumers, similar to married couples with a minimum of one Singaporean partner who are purchasing their second property so long as they intend to promote their first residential property. Lower the LTV limit on housing loans granted by monetary establishments regulated by MAS from 70% to 60% for property purchasers who are individuals with a number of outstanding housing loans on the time of the brand new housing purchase. Singapore Property Measures - 30 August 2010 The most popular seek for the number of bedrooms in Singapore is 4, followed by 2 and three. Lush Acres EC @ Sengkang

Discover out more about real estate funding in the area, together with info on international funding incentives and property possession. Many Singaporeans have been investing in property across the causeway in recent years, attracted by comparatively low prices. However, those who need to exit their investments quickly are likely to face significant challenges when trying to sell their property – and could finally be stuck with a property they can't sell. Career improvement programmes, in-house valuation, auctions and administrative help, venture advertising and marketing, skilled talks and traisning are continuously planned for the sales associates to help them obtain better outcomes for his or her shoppers while at Knight Frank Singapore. No change Present Rules

Extending the tax exemption would help. The exemption, which may be as a lot as $2 million per family, covers individuals who negotiate a principal reduction on their existing mortgage, sell their house short (i.e., for lower than the excellent loans), or take part in a foreclosure course of. An extension of theexemption would seem like a common-sense means to assist stabilize the housing market, but the political turmoil around the fiscal-cliff negotiations means widespread sense could not win out. Home Minority Chief Nancy Pelosi (D-Calif.) believes that the mortgage relief provision will be on the table during the grand-cut price talks, in response to communications director Nadeam Elshami. Buying or promoting of blue mild bulbs is unlawful.

A vendor's stamp duty has been launched on industrial property for the primary time, at rates ranging from 5 per cent to 15 per cent. The Authorities might be trying to reassure the market that they aren't in opposition to foreigners and PRs investing in Singapore's property market. They imposed these measures because of extenuating components available in the market." The sale of new dual-key EC models will even be restricted to multi-generational households only. The models have two separate entrances, permitting grandparents, for example, to dwell separately. The vendor's stamp obligation takes effect right this moment and applies to industrial property and plots which might be offered inside three years of the date of buy. JLL named Best Performing Property Brand for second year running

The data offered is for normal info purposes only and isn't supposed to be personalised investment or monetary advice. Motley Fool Singapore contributor Stanley Lim would not personal shares in any corporations talked about. Singapore private home costs increased by 1.eight% within the fourth quarter of 2012, up from 0.6% within the earlier quarter. Resale prices of government-built HDB residences which are usually bought by Singaporeans, elevated by 2.5%, quarter on quarter, the quickest acquire in five quarters. And industrial property, prices are actually double the levels of three years ago. No withholding tax in the event you sell your property. All your local information regarding vital HDB policies, condominium launches, land growth, commercial property and more

There are various methods to go about discovering the precise property. Some local newspapers (together with the Straits Instances ) have categorised property sections and many local property brokers have websites. Now there are some specifics to consider when buying a 'new launch' rental. Intended use of the unit Every sale begins with 10 p.c low cost for finish of season sale; changes to 20 % discount storewide; follows by additional reduction of fiftyand ends with last discount of 70 % or extra. Typically there is even a warehouse sale or transferring out sale with huge mark-down of costs for stock clearance. Deborah Regulation from Expat Realtor shares her property market update, plus prime rental residences and houses at the moment available to lease Esparina EC @ Sengkang
↑ One of the biggest reasons investing in a Singapore new launch is an effective things is as a result of it is doable to be lent massive quantities of money at very low interest rates that you should utilize to purchase it. Then, if property values continue to go up, then you'll get a really high return on funding (ROI). Simply make sure you purchase one of the higher properties, reminiscent of the ones at Fernvale the Riverbank or any Singapore landed property Get Earnings by means of Renting

In its statement, the singapore property listing - website link, government claimed that the majority citizens buying their first residence won't be hurt by the new measures. Some concessions can even be prolonged to chose teams of consumers, similar to married couples with a minimum of one Singaporean partner who are purchasing their second property so long as they intend to promote their first residential property. Lower the LTV limit on housing loans granted by monetary establishments regulated by MAS from 70% to 60% for property purchasers who are individuals with a number of outstanding housing loans on the time of the brand new housing purchase. Singapore Property Measures - 30 August 2010 The most popular seek for the number of bedrooms in Singapore is 4, followed by 2 and three. Lush Acres EC @ Sengkang

Discover out more about real estate funding in the area, together with info on international funding incentives and property possession. Many Singaporeans have been investing in property across the causeway in recent years, attracted by comparatively low prices. However, those who need to exit their investments quickly are likely to face significant challenges when trying to sell their property – and could finally be stuck with a property they can't sell. Career improvement programmes, in-house valuation, auctions and administrative help, venture advertising and marketing, skilled talks and traisning are continuously planned for the sales associates to help them obtain better outcomes for his or her shoppers while at Knight Frank Singapore. No change Present Rules

Extending the tax exemption would help. The exemption, which may be as a lot as $2 million per family, covers individuals who negotiate a principal reduction on their existing mortgage, sell their house short (i.e., for lower than the excellent loans), or take part in a foreclosure course of. An extension of theexemption would seem like a common-sense means to assist stabilize the housing market, but the political turmoil around the fiscal-cliff negotiations means widespread sense could not win out. Home Minority Chief Nancy Pelosi (D-Calif.) believes that the mortgage relief provision will be on the table during the grand-cut price talks, in response to communications director Nadeam Elshami. Buying or promoting of blue mild bulbs is unlawful.

A vendor's stamp duty has been launched on industrial property for the primary time, at rates ranging from 5 per cent to 15 per cent. The Authorities might be trying to reassure the market that they aren't in opposition to foreigners and PRs investing in Singapore's property market. They imposed these measures because of extenuating components available in the market." The sale of new dual-key EC models will even be restricted to multi-generational households only. The models have two separate entrances, permitting grandparents, for example, to dwell separately. The vendor's stamp obligation takes effect right this moment and applies to industrial property and plots which might be offered inside three years of the date of buy. JLL named Best Performing Property Brand for second year running

The data offered is for normal info purposes only and isn't supposed to be personalised investment or monetary advice. Motley Fool Singapore contributor Stanley Lim would not personal shares in any corporations talked about. Singapore private home costs increased by 1.eight% within the fourth quarter of 2012, up from 0.6% within the earlier quarter. Resale prices of government-built HDB residences which are usually bought by Singaporeans, elevated by 2.5%, quarter on quarter, the quickest acquire in five quarters. And industrial property, prices are actually double the levels of three years ago. No withholding tax in the event you sell your property. All your local information regarding vital HDB policies, condominium launches, land growth, commercial property and more

There are various methods to go about discovering the precise property. Some local newspapers (together with the Straits Instances ) have categorised property sections and many local property brokers have websites. Now there are some specifics to consider when buying a 'new launch' rental. Intended use of the unit Every sale begins with 10 p.c low cost for finish of season sale; changes to 20 % discount storewide; follows by additional reduction of fiftyand ends with last discount of 70 % or extra. Typically there is even a warehouse sale or transferring out sale with huge mark-down of costs for stock clearance. Deborah Regulation from Expat Realtor shares her property market update, plus prime rental residences and houses at the moment available to lease Esparina EC @ Sengkang

[Rockafellar-1] 1.0 ^1.1 One of the biggest reasons investing in a Singapore new launch is an effective things is as a result of it is doable to be lent massive quantities of money at very low interest rates that you should utilize to purchase it. Then, if property values continue to go up, then you'll get a really high return on funding (ROI). Simply make sure you purchase one of the higher properties, reminiscent of the ones at Fernvale the Riverbank or any Singapore landed property Get Earnings by means of Renting

In its statement, the singapore property listing - website link, government claimed that the majority citizens buying their first residence won't be hurt by the new measures. Some concessions can even be prolonged to chose teams of consumers, similar to married couples with a minimum of one Singaporean partner who are purchasing their second property so long as they intend to promote their first residential property. Lower the LTV limit on housing loans granted by monetary establishments regulated by MAS from 70% to 60% for property purchasers who are individuals with a number of outstanding housing loans on the time of the brand new housing purchase. Singapore Property Measures - 30 August 2010 The most popular seek for the number of bedrooms in Singapore is 4, followed by 2 and three. Lush Acres EC @ Sengkang

Discover out more about real estate funding in the area, together with info on international funding incentives and property possession. Many Singaporeans have been investing in property across the causeway in recent years, attracted by comparatively low prices. However, those who need to exit their investments quickly are likely to face significant challenges when trying to sell their property – and could finally be stuck with a property they can't sell. Career improvement programmes, in-house valuation, auctions and administrative help, venture advertising and marketing, skilled talks and traisning are continuously planned for the sales associates to help them obtain better outcomes for his or her shoppers while at Knight Frank Singapore. No change Present Rules

Extending the tax exemption would help. The exemption, which may be as a lot as $2 million per family, covers individuals who negotiate a principal reduction on their existing mortgage, sell their house short (i.e., for lower than the excellent loans), or take part in a foreclosure course of. An extension of theexemption would seem like a common-sense means to assist stabilize the housing market, but the political turmoil around the fiscal-cliff negotiations means widespread sense could not win out. Home Minority Chief Nancy Pelosi (D-Calif.) believes that the mortgage relief provision will be on the table during the grand-cut price talks, in response to communications director Nadeam Elshami. Buying or promoting of blue mild bulbs is unlawful.

A vendor's stamp duty has been launched on industrial property for the primary time, at rates ranging from 5 per cent to 15 per cent. The Authorities might be trying to reassure the market that they aren't in opposition to foreigners and PRs investing in Singapore's property market. They imposed these measures because of extenuating components available in the market." The sale of new dual-key EC models will even be restricted to multi-generational households only. The models have two separate entrances, permitting grandparents, for example, to dwell separately. The vendor's stamp obligation takes effect right this moment and applies to industrial property and plots which might be offered inside three years of the date of buy. JLL named Best Performing Property Brand for second year running

The data offered is for normal info purposes only and isn't supposed to be personalised investment or monetary advice. Motley Fool Singapore contributor Stanley Lim would not personal shares in any corporations talked about. Singapore private home costs increased by 1.eight% within the fourth quarter of 2012, up from 0.6% within the earlier quarter. Resale prices of government-built HDB residences which are usually bought by Singaporeans, elevated by 2.5%, quarter on quarter, the quickest acquire in five quarters. And industrial property, prices are actually double the levels of three years ago. No withholding tax in the event you sell your property. All your local information regarding vital HDB policies, condominium launches, land growth, commercial property and more

There are various methods to go about discovering the precise property. Some local newspapers (together with the Straits Instances ) have categorised property sections and many local property brokers have websites. Now there are some specifics to consider when buying a 'new launch' rental. Intended use of the unit Every sale begins with 10 p.c low cost for finish of season sale; changes to 20 % discount storewide; follows by additional reduction of fiftyand ends with last discount of 70 % or extra. Typically there is even a warehouse sale or transferring out sale with huge mark-down of costs for stock clearance. Deborah Regulation from Expat Realtor shares her property market update, plus prime rental residences and houses at the moment available to lease Esparina EC @ Sengkang

[2] One of the biggest reasons investing in a Singapore new launch is an effective things is as a result of it is doable to be lent massive quantities of money at very low interest rates that you should utilize to purchase it. Then, if property values continue to go up, then you'll get a really high return on funding (ROI). Simply make sure you purchase one of the higher properties, reminiscent of the ones at Fernvale the Riverbank or any Singapore landed property Get Earnings by means of Renting

In its statement, the singapore property listing - website link, government claimed that the majority citizens buying their first residence won't be hurt by the new measures. Some concessions can even be prolonged to chose teams of consumers, similar to married couples with a minimum of one Singaporean partner who are purchasing their second property so long as they intend to promote their first residential property. Lower the LTV limit on housing loans granted by monetary establishments regulated by MAS from 70% to 60% for property purchasers who are individuals with a number of outstanding housing loans on the time of the brand new housing purchase. Singapore Property Measures - 30 August 2010 The most popular seek for the number of bedrooms in Singapore is 4, followed by 2 and three. Lush Acres EC @ Sengkang

Discover out more about real estate funding in the area, together with info on international funding incentives and property possession. Many Singaporeans have been investing in property across the causeway in recent years, attracted by comparatively low prices. However, those who need to exit their investments quickly are likely to face significant challenges when trying to sell their property – and could finally be stuck with a property they can't sell. Career improvement programmes, in-house valuation, auctions and administrative help, venture advertising and marketing, skilled talks and traisning are continuously planned for the sales associates to help them obtain better outcomes for his or her shoppers while at Knight Frank Singapore. No change Present Rules

Extending the tax exemption would help. The exemption, which may be as a lot as $2 million per family, covers individuals who negotiate a principal reduction on their existing mortgage, sell their house short (i.e., for lower than the excellent loans), or take part in a foreclosure course of. An extension of theexemption would seem like a common-sense means to assist stabilize the housing market, but the political turmoil around the fiscal-cliff negotiations means widespread sense could not win out. Home Minority Chief Nancy Pelosi (D-Calif.) believes that the mortgage relief provision will be on the table during the grand-cut price talks, in response to communications director Nadeam Elshami. Buying or promoting of blue mild bulbs is unlawful.

A vendor's stamp duty has been launched on industrial property for the primary time, at rates ranging from 5 per cent to 15 per cent. The Authorities might be trying to reassure the market that they aren't in opposition to foreigners and PRs investing in Singapore's property market. They imposed these measures because of extenuating components available in the market." The sale of new dual-key EC models will even be restricted to multi-generational households only. The models have two separate entrances, permitting grandparents, for example, to dwell separately. The vendor's stamp obligation takes effect right this moment and applies to industrial property and plots which might be offered inside three years of the date of buy. JLL named Best Performing Property Brand for second year running

The data offered is for normal info purposes only and isn't supposed to be personalised investment or monetary advice. Motley Fool Singapore contributor Stanley Lim would not personal shares in any corporations talked about. Singapore private home costs increased by 1.eight% within the fourth quarter of 2012, up from 0.6% within the earlier quarter. Resale prices of government-built HDB residences which are usually bought by Singaporeans, elevated by 2.5%, quarter on quarter, the quickest acquire in five quarters. And industrial property, prices are actually double the levels of three years ago. No withholding tax in the event you sell your property. All your local information regarding vital HDB policies, condominium launches, land growth, commercial property and more

There are various methods to go about discovering the precise property. Some local newspapers (together with the Straits Instances ) have categorised property sections and many local property brokers have websites. Now there are some specifics to consider when buying a 'new launch' rental. Intended use of the unit Every sale begins with 10 p.c low cost for finish of season sale; changes to 20 % discount storewide; follows by additional reduction of fiftyand ends with last discount of 70 % or extra. Typically there is even a warehouse sale or transferring out sale with huge mark-down of costs for stock clearance. Deborah Regulation from Expat Realtor shares her property market update, plus prime rental residences and houses at the moment available to lease Esparina EC @ Sengkang

[1]

[2]

@@ Line 1: / Line 1: @@
-I'm Everette (18) from Calgary, Canada. <br>I'm learning Korean literature at a local high school and I'm just about to graduate.<br>I have a part time job in a post office.<br>xunjie 小売分野に従事する職員があります。
+In [[financial mathematics]], a '''deviation risk measure''' is a function to quantify [[financial risk]] (and not necessarily [[downside risk]]) in a different method than a general [[risk measure]].  Deviation risk measures generalize the concept of [[standard deviation]].
-世界デンマークのジュエリーブランドPANDORA（パンドラ）の女性に好ま記事REVIEW 2013年8月23日、
-ティファニーは我々の不満を共有しないと、 [http://bvlgarishop.sd27dpac.com/ ���� �Хå� ��ǥ��`��] あなたが決定されるように！ブラスト福小鵬日：2013年8月24日12時06分34秒メアリーPはこの数字を持っていた。
+==Mathematical definition==
-氏はチャクラは免税品のリストに含まれてなど、
+A function <math>D: \mathcal{L}^2 \to [0,+\infty]</math>, where <math>\mathcal{L}^2</math> is the [[L2 space]] of [[random variable|random]] [[Portfolio (finance)|portfolio returns]], is a deviation risk measure if
-ヤギのミルクメーターパビリオン側面図·杭州歌っベビー用品有限公司は進歩しているしてみましょう。 [http://www.rheintalverlag.ch/newsletter/gaga.php �����ߥ�� �rӋ] 民間の通りhuangqiao家庭繊維有限極細竹繊維の糸加工技術や製品の研究を開始し、
+# Shift-invariant: <math>D(X + r) = D(X)</math> for any <math>r \in \mathbb{R}</math>
-佛山市の旧活況縫製工場は、
+# Normalization: <math>D(0) = 0</math>
-常に彼のデザインの布の要件を要求しており、[http://3kydd.com/bio/pdfs/dr.martens.php UGG �֩`�� ���`���ȥ�ꥢ] 同じ女性の愛とランジェリーの下着のさまざまな段階にあるために詩曼芬下着の女性は、
+# Positively homogeneous: <math>D(\lambda X) = \lambda D(X)</math> for any <math>X \in \mathcal{L}^2</math> and <math>\lambda > 0</math>
-リタオラカメオDKNYモデルホット歌手リタ·オラを参照してくださいスーパーモデルのスポークスマンのDKNYは、
+# Sublinearity: <math>D(X + Y) \leq D(X) + D(Y)</math> for any <math>X, Y \in \mathcal{L}^2</math>
-翻訳：魚日付なしの中国アパレルネットワーク劉Fangfang浅瀬：近い女性教授の本来の目的は、
+# Positivity: <math>D(X) > 0</math> for all nonconstant ''X'', and <math>D(X) = 0</math> for any constant ''X''.<ref name="Rockafellar">{{cite journal|title=Deviation Measures in Risk Analysis and Optimization|first1=Tyrrell|last1=Rockafellar|first2=Stanislav|last2=Uryasev|first3=Michael|last3=Zabarankin|year=2002|url=http://papers.ssrn.com/sol3/papers.cfm?abstract_id=365640|accessdate=January 15, 2012}}</ref><ref>{{cite journal|title=Progress in Risk Measurement|first1=Siwei|last1=Cheng|first2=Yanhui|last2=Liu|first3=Shouyang|last3=Wang|year=2004|journal=Advanced Modelling and Optimization|volume=6|number=1}}</ref>
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+==Relation to risk measure==
+There is a [[bijection|one-to-one]] relationship between a deviation risk measure ''D'' and an expectation-bounded [[risk measure]] ''R'' where for any <math>X \in \mathcal{L}^2</math>
+* <math>D(X) = R(X - \mathbb{E}[X])</math>
+* <math>R(X) = D(X) - \mathbb{E}[X]</math>.
+''R'' is expectation bounded if <math>R(X) > \mathbb{E}[-X]</math> for any nonconstant ''X'' and <math>R(X) = \mathbb{E}[-X]</math> for any constant ''X''.
+If <math>D(X) < \mathbb{E}[X] - \operatorname{ess\inf} X</math> for every ''X'' (where <math>\operatorname{ess\inf}</math> is the [[essential infimum]]), then there is a relationship between ''D'' and a [[coherent risk measure]].<ref name="Rockafellar" />
+==Examples==
+{{stub-section|examples of measures other than stdev|date=May 2013}}
+The [[standard deviation]] is clearly a deviation risk measure.
+==References==
+{{Reflist}}
+[[Category:Mathematical finance]]
+[[Category:Financial risk]]

Tschuprow's T: Difference between revisions

Latest revision as of 04:56, 21 March 2013

Contents

Mathematical definition

Relation to risk measure

Examples

References

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Tschuprow's T: Difference between revisions

Latest revision as of 04:56, 21 March 2013

Mathematical definition

Relation to risk measure

Examples

References

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