Multidimensional Poverty Index - Revision history

158.143.136.222: /* Indicators used */

2015-01-07T18:12:33Z

Indicators used

← Older revision		Revision as of 20:12, 7 January 2015
Line 1:		Line 1:
	~~{{Technical\|date=August 2013}}~~
	The '''bid–ask matrix''' is a [[matrix (mathematics)\|matrix]] with elements corresponding with exchange rates between the [[assets]]. These rates are in ''physical units'' (e.g. number of stocks) and not with respect to any ''[[numeraire]]''. The <math>(i,j)</math> element of the matrix is the number of units of asset <math>i</math> which can be exchanged for 1 unit of asset <math>j</math>.

	~~==Mathematical Definition==~~
	~~A <math>d \times d</math> matrix <math>\Pi = \left[\pi_{ij}\right]_{1 \leq i,j \leq d}</math> is a ''bid-ask matrix'', if~~
	~~# <math>\pi_{ij} > 0</math> for <math>1 \leq i,j \leq d</math>. Any trade has a positive exchange rate.~~
	~~# <math>\pi_{ii} = 1</math> for <math>1 \leq i \leq d</math>. Can always trade 1 unit with itself.~~
	# <math>\pi_{ij} \leq \pi_{ik}\pi_{kj}</math> for <math>1 \leq i,j,k \leq d</math>. A direct exchange is always at most as expensive as a chain of exchanges.<ref name="WS02">{{cite journal\|last=Schachermayer\|first=Walter\|date=November 15, 2002\|title=The Fundamental Theorem of Asset Pricing under Proportional Transaction Costs in Finite Discrete Time}}</ref>

	~~==Example==~~		Slider WindowWhen you're looking for credible movers, talking with your windows with [http://photobucket.com/images/Windows Windows] and Doors If you have any inquiries regarding in which and how to use garden windows for sale - [http://Unitedreplacementwindows.Decaturilmetalbuildings.com/casement-garden-windows-for-sale-online/ Highly recommended Resource site],, you can call us at the page. .
	~~Assume a market with 2 assets (A and B), such that <math>x</math> units of A can be exchanged~~ for ~~1 unit of B~~, ~~and <math>y</math> units of B can be exchanged for 1 unit of A. Then the ''bid–ask matrix'' <math>\Pi</math> is~~:

	~~: <math>\Pi = \begin{bmatrix}~~
	~~1 & x \\~~
	~~y & 1~~
	~~\end{bmatrix}<~~/~~math>~~

	~~==Relation to solvency cone==~~
	~~If given a bid–ask matrix <math>\Pi<~~/~~math> for <math>d<~~/~~math> assets such that <math>\Pi = \left(\pi^{ij}\right)_{1 \leq i,j \leq d}<~~/~~math>~~ and ~~<math>m \leq d</math> is the number of assets~~ which ~~with any non~~-~~negative quantity of them can be "discarded" (traditionally <math>m = d<~~/~~math>)~~. ~~Then the [[solvency cone]] <math>K(\Pi) \subset \mathbb{R}^d<~~/~~math> is the convex cone spanned by the unit vectors <math>e^i, 1 \leq i \leq m</math> and the vectors <math>\pi^{ij}e^i~~-~~e^j, 1 \leq i,j \leq d<~~/~~math>.<ref name="WS02" />~~

	~~Similarly given a (constant) solvency cone it is possible to extract the bid–ask matrix from the bounding vectors.~~

	~~==Notes==~~
	* The [[bid–ask spread]] ~~for pair <math>(i~~,~~j)</math> is <math>\left\{\frac{1}{\pi_{ji}}~~,~~\pi_{ij}\right\}</math>~~.
	* If <math>\pi_{ij} = \frac{1}{\pi_{ji}}</math> then that pair is [[frictionless market\|frictionless]].

	~~==References==~~
	~~{{Reflist}}~~

	~~{{DEFAULTSORT:Bid-ask matrix}}~~
	~~[[Category:Mathematical finance]]~~

92.37.69.151: /* MPI in some developing countries */ Slovenia is a developed, not developing state.

2013-06-28T17:47:50Z

MPI in some developing countries: Slovenia is a developed, not developing state.

← Older revision		Revision as of 19:47, 28 June 2013
Line 1:		Line 1:
	~~One of the first things you’ll realize if you maintain the Sibert is that it is heavy! Weighing 12 ounces, it~~ is a ~~tank and, given its army design, is fitting. This knife is for tremendous heavy responsibility users and~~ [~~http://Ads.it5.in/education-learning/online-education-training-coaching/sog-field-pup-ii-knife-review_i12723 military personnel~~] ~~solely~~. ~~The load makes it too heavy to be an EDC~~ in my e~~-book~~. ~~The Delica4, the fourth installment~~ of ~~the Delica collection, is certainly one of Spyderco’s most popular~~ and ~~best selling knife. The knife is~~ [~~http://96.21.43.7510101/mediawiki/index.php/Sog_Knives_Spirit_Review ultra gentle~~] ~~weight at 2.5oz and perfect for EDC. Different, more heavy duty knives, can deal with harder tasks but the Delica4′s VG-10 steel permits it to resist harsh work if wanted~~.<br><br>~~That~~ is ~~an awesome low budget knife. It [http://Indieroulette.com/index.php?title=Sog_Bowie_Knife_Review positively] seems like it's up for any job and its efficiency is as much as par. The traces on~~ the ~~handle give it an awesome look and nice consolation. It's thicker giving a better certain grip for me. Are you a fan~~ of the Hinderer? Nicely you’ll need to get your fingers on this basic Rick Hinderer design SpeedSafe spring assisted knife. It has a pleasant contact with both the steel and handle having a titanium carbo-nitride coating. It is a framelock folding knife with a Hinderer Lockbar stabilizer.<br><br>Victorinox Swiss Army Traditional SD Pocket Knife (Blue), good sale Dehumidifiers You should buy Victorinox Swiss Army Classic SD Pocket Knife (Blue) see full Review. We expect you discover Cheap Value and in the present day Outlets Buy Online delivery options accessible and extra info by way of ~~click [http:~~/~~/abcnews~~.~~go.com~~/~~blogs~~/~~politics/2013/03/tsa-to-allow-pocket-knives-on-planes/ case knife] the hyperlink below – Safe Check out. Avaliable at Amazon.com It~~ is a ~~knife that can take some abuse. From the stable RotoLock mechanism to the prime quality Elmax PM one hundred seventy metal on the 4.5mm thick blade~~, ~~you can belief this knife to come via~~ for ~~you. The handles are CNC machined perpendicular to the blades size to ensure a nice stable grip on the knife.~~<br><br>~~Buck 110 is a classic knife that has been round for a number of many years now~~. It has a ~~three~~.25” carbon metal blade that is extraordinarily proof against corrosion and rust. The deployment is the old system of pulling the blade out with no reliance on shifting elements or know-how. Of all [http://~~www~~.~~knifecenter~~.~~com~~/~~knifecenter~~/~~index/foldersm~~.~~html knife sales] the knives on this listing, the Benchmade Mini Griptilian~~ is ~~the greatest folding knife in our opinion. It has the precise mix~~ of ~~excellent design and a durable blade that makes it easy to use and comfy on the same time~~.<br><br>~~The Gerber EAB Lite is~~ a ~~[http://wiki.Tes.Mi.it/mediawiki/index.php/Sog_St-04_Automatic_Knife_Review replaceable utility] knife that can accommodate any normal~~ 2~~.25″ blade. When no blade has been fitted to it~~, ~~it may be comfortably folded and stowed away. The handle is equipped with finger grooves that enable for a secure grip. The deal with additionally incorporates a clip~~ that can be ~~used to clip it on to your pocket or your belt. The EAB Lite is ideal~~ for ~~basic utility or construction work like opening bins, chopping drywall~~, and ~~so on~~. ~~Whereas Gerber blades are a very good match for~~ the ~~knife, you should be cautious utilizing other blades within the EAB Lite.~~<br><br>~~The Delica4′s deal with~~ is made from Spyderco’s traditional Bi-Directional Texturing that's featured on a number of their knives. The texturing provides you grip in a very comfortable and ergonomic method. The handle has steel liners that adds a feeling of stability to ~~the knife when you use it. The deal with also has~~ a ~~pivot screw~~ that ~~allows you to adjust the screw if the blade turns into free. Deciding on the suitable tactical pocket knife is about function, desire~~, and individual requirements including hand measurement. The proper knife for one individual could not work for an additional because of bodily causes or due to the rationale the second individual wants the knife.<br><br>~~I always love an excellent deal on a pocket knife and this proved such. Victorinox~~ is ~~a highly respected brand and~~ the ~~standard~~ of ~~the knife is second to none. A terrific knife to carry or hold in your desk. They're centered totally on slip~~-joint knives, so in case you wanta good cooperhead, stockman, peanut or atrapper, then Case pocket knives are the best choice. They will costyou slightly extra, but in return you will get a top quality Case best pocketknife. Must be ~~sturdy sufficient, that ought to the worst case state of affairs happen, I would feel assured in utilizing the knife in the wild to survive.~~<br><br>~~The Rescue Knife can’t really compete with these different knives by way of materials, high quality of construction or options~~. ~~But in~~ the ~~case of easy chopping, this knife~~ is ~~a contender. Within~~ the ~~Loop tests, we had been shocked at how properly~~ the ~~Rescue Knife sliced via all take a look at supplies but the Amsteel with a single pull~~, and the ~~Amsteel took solely two pulls. The graceful~~, ~~wavy serrations appear to be the important thing in not getting tangled in the nest of frayed excessive-tech fibers. While it didn’t perform quite as well within the Wrap assessments~~, ~~it nonetheless held its personal among its larger-priced opponents.~~<br><br>~~As I usually do when looking to decide~~ a ~~few of these factors~~ is ~~I flip~~ to ~~Amazon~~.~~com who seem to carry just about all the pieces along with a excessive number of customer reviews~~, ~~rankings and [http:~~//~~Wiki~~.~~Shol.ru~~/~~index.php/Sog_Seal_Knife_Review_2000 descriptions~~]. ~~It helps when making an attempt to decide on one thing or the opposite. I did this with the abnormal pocket knife to see what turns up. This can~~ [~~http~~:~~//www.thebestpocketknifereviews.com/sog-knives-review/ SOG Knives Reviews~~] be a collaboration knife between two large knife producers Spyderco Knives and Lion Metal Knives Some may say it has a number of the best designs you can search for in a knife. It seems to be like the SR-1, but has some Spyderco features just like the Spydie gap.		{{Technical\|date=August 2013}}
			The '''bid–ask matrix''' is a [[matrix (mathematics)\|matrix]] with elements corresponding with exchange rates between the [[assets]]. These rates are in ''physical units'' (e.g. number of stocks) and not with respect to any ''[[numeraire]]''. The <math>(i,j)</math> element of the matrix is the number of units of asset <math>i</math> which can be exchanged for 1 unit of asset <math>j</math>.

			==Mathematical Definition==
			A <math>d \times d</math> matrix <math>\Pi = \left[\pi_{ij}\right]_{1 \leq i,j \leq d}</math> is a ''bid-ask matrix'', if
			# <math>\pi_{ij} > 0</math> for <math>1 \leq i,j \leq d</math>. Any trade has a positive exchange rate.
			# <math>\pi_{ii} = 1</math> for <math>1 \leq i \leq d</math>. Can always trade 1 unit with itself.
			# <math>\pi_{ij} \leq \pi_{ik}\pi_{kj}</math> for <math>1 \leq i,j,k \leq d</math>. A direct exchange is always at most as expensive as a chain of exchanges.<ref name="WS02">{{cite journal\|last=Schachermayer\|first=Walter\|date=November 15, 2002\|title=The Fundamental Theorem of Asset Pricing under Proportional Transaction Costs in Finite Discrete Time}}</ref>

			==Example==
			Assume a market with 2 assets (A and B), such that <math>x</math> units of A can be exchanged for 1 unit of B, and <math>y</math> units of B can be exchanged for 1 unit of A. Then the ''bid–ask matrix'' <math>\Pi</math> is:

			: <math>\Pi = \begin{bmatrix}
			1 & x \\
			y & 1
			\end{bmatrix}</math>

			==Relation to solvency cone==
			If given a bid–ask matrix <math>\Pi</math> for <math>d</math> assets such that <math>\Pi = \left(\pi^{ij}\right)_{1 \leq i,j \leq d}</math> and <math>m \leq d</math> is the number of assets which with any non-negative quantity of them can be "discarded" (traditionally <math>m = d</math>). Then the [[solvency cone]] <math>K(\Pi) \subset \mathbb{R}^d</math> is the convex cone spanned by the unit vectors <math>e^i, 1 \leq i \leq m</math> and the vectors <math>\pi^{ij}e^i-e^j, 1 \leq i,j \leq d</math>.<ref name="WS02" />

			Similarly given a (constant) solvency cone it is possible to extract the bid–ask matrix from the bounding vectors.

			==Notes==
			* The [[bid–ask spread]] for pair <math>(i,j)</math> is <math>\left\{\frac{1}{\pi_{ji}},\pi_{ij}\right\}</math>.
			* If <math>\pi_{ij} = \frac{1}{\pi_{ji}}</math> then that pair is [[frictionless market\|frictionless]].

			==References==
			{{Reflist}}

			{{DEFAULTSORT:Bid-ask matrix}}
			[[Category:Mathematical finance]]

24.103.44.10: /* Indicators */ Removed unnecessary redundancy of dimension weighting explanation.

2012-08-06T16:53:09Z

Indicators: Removed unnecessary redundancy of dimension weighting explanation.

New page

One of the first things you’ll realize if you maintain the Sibert is that it is heavy! Weighing 12 ounces, it is a tank and, given its army design, is fitting. This knife is for tremendous heavy responsibility users and [http://Ads.it5.in/education-learning/online-education-training-coaching/sog-field-pup-ii-knife-review_i12723 military personnel] solely. The load makes it too heavy to be an EDC in my e-book. The Delica4, the fourth installment of the Delica collection, is certainly one of Spyderco’s most popular and best selling knife. The knife is [http://96.21.43.7510101/mediawiki/index.php/Sog_Knives_Spirit_Review ultra gentle] weight at 2.5oz and perfect for EDC. Different, more heavy duty knives, can deal with harder tasks but the Delica4′s VG-10 steel permits it to resist harsh work if wanted. That is an awesome low budget knife. It [http://Indieroulette.com/index.php?title=Sog_Bowie_Knife_Review positively] seems like it's up for any job and its efficiency is as much as par. The traces on the handle give it an awesome look and nice consolation. It's thicker giving a better certain grip for me. Are you a fan of the Hinderer? Nicely you’ll need to get your fingers on this basic Rick Hinderer design SpeedSafe spring assisted knife. It has a pleasant contact with both the steel and handle having a titanium carbo-nitride coating. It is a framelock folding knife with a Hinderer Lockbar stabilizer. Victorinox Swiss Army Traditional SD Pocket Knife (Blue), good sale Dehumidifiers You should buy Victorinox Swiss Army Classic SD Pocket Knife (Blue) see full Review. We expect you discover Cheap Value and in the present day Outlets Buy Online delivery options accessible and extra info by way of click [http://abcnews.go.com/blogs/politics/2013/03/tsa-to-allow-pocket-knives-on-planes/ case knife] the hyperlink below – Safe Check out. Avaliable at Amazon.com It is a knife that can take some abuse. From the stable RotoLock mechanism to the prime quality Elmax PM one hundred seventy metal on the 4.5mm thick blade, you can belief this knife to come via for you. The handles are CNC machined perpendicular to the blades size to ensure a nice stable grip on the knife. Buck 110 is a classic knife that has been round for a number of many years now. It has a three.25” carbon metal blade that is extraordinarily proof against corrosion and rust. The deployment is the old system of pulling the blade out with no reliance on shifting elements or know-how. Of all [http://www.knifecenter.com/knifecenter/index/foldersm.html knife sales] the knives on this listing, the Benchmade Mini Griptilian is the greatest folding knife in our opinion. It has the precise mix of excellent design and a durable blade that makes it easy to use and comfy on the same time. The Gerber EAB Lite is a [http://wiki.Tes.Mi.it/mediawiki/index.php/Sog_St-04_Automatic_Knife_Review replaceable utility] knife that can accommodate any normal 2.25″ blade. When no blade has been fitted to it, it may be comfortably folded and stowed away. The handle is equipped with finger grooves that enable for a secure grip. The deal with additionally incorporates a clip that can be used to clip it on to your pocket or your belt. The EAB Lite is ideal for basic utility or construction work like opening bins, chopping drywall, and so on. Whereas Gerber blades are a very good match for the knife, you should be cautious utilizing other blades within the EAB Lite. The Delica4′s deal with is made from Spyderco’s traditional Bi-Directional Texturing that's featured on a number of their knives. The texturing provides you grip in a very comfortable and ergonomic method. The handle has steel liners that adds a feeling of stability to the knife when you use it. The deal with also has a pivot screw that allows you to adjust the screw if the blade turns into free. Deciding on the suitable tactical pocket knife is about function, desire, and individual requirements including hand measurement. The proper knife for one individual could not work for an additional because of bodily causes or due to the rationale the second individual wants the knife. I always love an excellent deal on a pocket knife and this proved such. Victorinox is a highly respected brand and the standard of the knife is second to none. A terrific knife to carry or hold in your desk. They're centered totally on slip-joint knives, so in case you wanta good cooperhead, stockman, peanut or atrapper, then Case pocket knives are the best choice. They will costyou slightly extra, but in return you will get a top quality Case best pocketknife. Must be sturdy sufficient, that ought to the worst case state of affairs happen, I would feel assured in utilizing the knife in the wild to survive. The Rescue Knife can’t really compete with these different knives by way of materials, high quality of construction or options. But in the case of easy chopping, this knife is a contender. Within the Loop tests, we had been shocked at how properly the Rescue Knife sliced via all take a look at supplies but the Amsteel with a single pull, and the Amsteel took solely two pulls. The graceful, wavy serrations appear to be the important thing in not getting tangled in the nest of frayed excessive-tech fibers. While it didn’t perform quite as well within the Wrap assessments, it nonetheless held its personal among its larger-priced opponents. As I usually do when looking to decide a few of these factors is I flip to Amazon.com who seem to carry just about all the pieces along with a excessive number of customer reviews, rankings and [http://Wiki.Shol.ru/index.php/Sog_Seal_Knife_Review_2000 descriptions]. It helps when making an attempt to decide on one thing or the opposite. I did this with the abnormal pocket knife to see what turns up. This can [http://www.thebestpocketknifereviews.com/sog-knives-review/ SOG Knives Reviews] be a collaboration knife between two large knife producers Spyderco Knives and Lion Metal Knives Some may say it has a number of the best designs you can search for in a knife. It seems to be like the SR-1, but has some Spyderco features just like the Spydie gap.