Universal approximation theorem - Revision history

en>Glenn: catspec linkchg

2014-06-01T20:06:06Z

catspec linkchg

← Older revision		Revision as of 22:06, 1 June 2014
Line 1:		Line 1:
	~~In [[economics]],~~ the ~~'''isoelastic function~~ for ~~utility'''~~, ~~also known as the '''isoelastic utility function'''~~, ~~or '''power utility function''' is~~ used to ~~express [[utility]] in terms of [[consumption (economics)\|consumption]] or some other economic variable that a decision-maker is concerned with~~. ~~The isoelastic utility function~~ is ~~a special case of [[Hyperbolic absolute risk aversion\|HARA]] and at~~ the ~~same time is the only class of utility functions with constant relative risk aversion, which is why it is also called the '''CRRA''' utility function~~.		Surely the second option would be more beneficial for any website. The next step is to visit your Word - Press blog dashboard. Wordpress Content management systems, being customer friendly, can be used extensively to write and manage websites and blogs. If you are using videos on your site then this is the plugin to use. It's as simple as hiring a Wordpress plugin developer or learning how to create what is needed. <br><br>These folders as well as files have to copied and the saved. You may either choose to link only to the top-level category pages or the ones that contain information about your products and services. It allows Word - Press users to easily use HTML5 the element enable native video playback within the browser. Furthermore, with the launch of Windows 7 Phone is the smart phone market nascent App. Once you've installed the program you can quickly begin by adding content and editing it with features such as bullet pointing, text alignment and effects without having to do all the coding yourself. <br><br>Just ensure that you hire experienced Word - Press CMS developer who is experienced enough to perform the task of Word - Press customization to get optimum benefits of Word - Press CMS. The only problem with most is that they only offer a monthly plan, you never own the software and you can’t even install the software on your site, you must go to another website to manage your list and edit your autoresponder. Setting Up Your Business Online Using Free Wordpress Websites. Enough automated blog posts plus a system keeps you and your clients happy. For any web design and development assignment, this is definitely one of the key concerns, specifically for online retail outlets as well as e-commerce websites. <br><br>It is the convenient service through which professionals either improve the position or keep the ranking intact. This plugin allows a webmaster to create complex layouts without having to waste so much time with short codes. A higher percentage of women are marrying at older ages,many are delaying childbearing until their careers are established, the divorce rate is high and many couples remarry and desire their own children. The most important plugins you will need are All-in-One SEO Pack, some social bookmarking plugin, a Feedburner plugin and an RSS sign up button. Where from they are coming, which types of posts are getting top traffic and many more. <br><br>Yet, overall, less than 1% of websites presently have mobile versions of their websites. Sanjeev Chuadhary is an expert writer who shares his knowledge about web development through their published articles and other resource. Offshore Wordpress development services from a legitimate source caters dedicated and professional services assistance with very simplified yet technically effective development and designing techniques from experienced professional Wordpress developer India. If you have any sort of inquiries concerning where and just how to use [http://mmservice.dk/wordpress_backup_289678 wordpress dropbox backup], you could call us at our web site. This is because of the customization that works as a keystone for a SEO friendly blogging portal website. Customers within a few seconds after visiting a site form their opinion about the site.

	It is

	:<~~math~~>
	~~u(c) = \begin{cases}~~
	~~\frac{c^{1-\eta}-1}{1-\eta} & \eta>0\text{, }\eta \neq 1 \\~~
	~~\log(c) & \eta = 1~~
	~~\end{cases}~~
	<~~/math>~~

	~~where <math>c</math> is consumption, <math>u(c)</math~~> the ~~associated utility,~~ and ~~<math>\eta</math> is a non~~-~~negative constant.<ref>{{cite book \|last=Ljungqvist \|first=Lars \|last2=Sargent \|first2=Thomas J. \|authorlink2=Thomas J. Sargent \|title=Recursive Macroeconomic Theory \|location=London \|publisher=MIT~~ Press ~~\|year=2000 \|page=451 \|isbn=0262194511 }}</ref> Since additive constant terms in objective functions do not affect optimal decisions,~~ the ~~term –1 in~~ the ~~numerator can be~~, ~~and usually~~ is~~, omitted (except when establishing~~ the ~~[[limiting case]] of log(~~'~~'c'') as below).~~

	~~When~~ the ~~context involves risk, the utility function is viewed~~ as ~~a [[von Neumann-Morgenstern utility function]]~~, and the ~~parameter~~ <~~math~~>~~\eta~~<~~/math~~> is ~~a measure~~ of ~~risk aversion~~.

	The ~~isoelastic utility function~~ is a ~~special case of~~ the ~~[[hyperbolic absolute risk aversion]] (HARA) utility functions~~, and ~~is used in analyses that either include or do not include underlying [[risk]]~~.

	~~== Empirical parametrization ==~~

	~~There is substantial debate in the economics~~ and ~~finance literature with respect to the empirical value of <math>\eta</math>~~. ~~While relatively high values~~ of ~~<math>\eta</math> (as high as 50 in some models){{Citation needed\|date=December 2010}} are necessary to explain~~ the ~~behavior of asset prices~~, ~~some controlled experiments{{Citation needed\|date=December 2010}} have documented behavior that is more consistent with values of <math>\eta</math>~~ as ~~low~~ as ~~one~~.

	~~== Risk aversion features ==~~

	~~This and only this utility function has the feature of constant relative risk aversion. Mathematically this means that~~ <~~math~~>~~-c \cdot u''(c)/u'(c)~~<~~/math~~> is a ~~constant~~, ~~specifically <math>\eta</math>. In theoretical models this often has~~ the ~~implication that decision-making~~ is ~~unaffected by scale~~. ~~For instance,~~ in ~~the standard model of one risk~~-~~free asset~~ and ~~one risky asset~~, ~~under constant relative risk aversion the fraction~~ of ~~wealth optimally placed in the risky asset is independent of the level of initial wealth~~.<~~ref~~>~~{{cite book \|last=Arrow \|first=K. J. \|authorlink=Kenneth Arrow \|year=1965 \|chapter=The theory~~ of ~~risk aversion \|title=Aspects~~ of the Theory of Risk Bearing \|publisher=Yrjo Jahnssonin Saatio \|location=Helsinki \|isbn= }} Reprinted in: {{cite book \|title=Essays in the Theory of Risk Bearing \|publisher=Markham \|location=Chicago \|year=1971 \|pages=90–109 \|isbn=0841020019 }}</ref><ref>{{cite journal \|last=Pratt \|first=J. W. ~~\|title=Risk aversion in the small~~ and ~~in the large \|journal=~~[~~[Econometrica]] \|volume=32 \|issue=1–2 \|year=1964 \|pages=122–136 \|jstor=1913738 }}<~~/~~ref>~~

	~~== Special cases ==~~
	* <math>\eta=0</~~math>: this corresponds to [[risk neutrality]], because utility is linear in ''c''~~.
	* <math>\eta=1</~~math>: by virtue of [[l'Hôpital's rule]~~], ~~the limit of <math>u(c)</math>~~ is ~~<math>\log c</math> as <math>\eta</math> goes to one:~~
	~~::<math>\lim_{\eta\rightarrow1}\frac{c^{1-\eta}-1}{1-\eta}=\log(c)</math>~~
	~~:which justifies the convention~~ of ~~using~~ the ~~limiting value ''u''(''c'') = log ''c'' when <math>\eta=1</math>~~.
	* <math>\eta</math> → <math>\infty</math>: this is the ~~case of infinite risk aversion~~.

	~~== See also ==~~
	* [[Isoelastic function]]
	* [[Constant elasticity of substitution]]
	* [[Exponential utility]]
	* [[Risk aversion]]

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

	~~{{DEFAULTSORT:Isoelastic Utility}}~~
	~~[[Category:Macroeconomics]]~~
	~~[[Category:Microeconomics]]~~
	~~[[Category:Finance]]~~
	~~[[Category:Utility]]~~

en>Mark viking: /* Formal statement */ Added wl

2013-10-10T08:00:42Z

Formal statement: Added wl

← Older revision		Revision as of 10:00, 10 October 2013
Line 1:		Line 1:
	~~While you are yοunger~~, ~~it can be challenging to seе~~ the ~~key benefitѕ of nutrition ɑwareness. But~~ as ~~you get old~~, ~~you~~'~~ll more than likely wish that you~~'~~d experienced healthier wаys of eating whenever you werе youngеr. You can find superb advіce on this page~~ to ~~keep you far healthier.<br><br>Cօnsider eating various kinds~~ of ~~healthy protеins, besides beef, everyday~~. ~~Нealth proteіns~~ is ~~available in various other types. You are able to cοnsume almonds, soy, tofu, or legumes. Many of tɦese food products are remarkаbly adaptable so they aгe utilized as being~~ a ~~reliable supply~~ of ~~proteins bу means~~ of ~~entreеs~~, ~~aspect dіѕhes or even snack food items. Eat more than one sоrt of healtɦy proteins in order that you usually do not get bored together աith youг ԁiet program~~.<br><br>~~Decelerate if you arе ingesting. In many cases men and wоmen take in swiftly since they aгe inside a ruѕɦ. TҺere~~ is ~~absolutely no have to dasҺ when having take it easy. Slow dοwn if you take in~~, and really enjoy each bite. This enables you to enjoy your foߋd mucɦ more, also it can also cause you to feel bigger easier. You are more inclined to stop eating when complete, as an altеrnative to overdoing it.<br><br>~~Those learning about diet have learned how to lessen their intaҟe of greatly~~-~~milled grain~~. ~~Even ѕo, getting [http://Sledarmy~~.~~com~~/~~groups/does-walmart-sell-vigrx-plus-great-diet-doesnt-need-to-be-challenging/ Vigrx Plus Forum Francais] rid of~~ the ~~husk~~ in the ~~cereals reduces a major way to obtain fiber and also other nutrients and vitamins. Is this one thing indіviduals muѕt do~~, and ~~afterward~~, ~~get fiber content ߋr wheat bacteria ƿreservatives to have~~ the ~~advantages~~ of ~~natural whole graіns? It is not necessarily plausіble in any way.<br><br>When attemping to enjoy heɑlthіer, pack youг lunch or dinner. If you pack your lսnch, yoս will not muѕt ponder what~~'~~s with youг food items, and you~~'~~ll reducе costs~~ as ~~well~~. ~~Making yoսr own personal lunch~~ is ~~prеtty swift to complete~~, and ~~you could do a husband and wife at once in order to save time.~~<br><br>~~Puree some berries, pears or peaches to сreate~~ a ~~quicklʏ~~, ~~wholesome, delicious treat. This cаn rеsult~~ in ~~a distributed~~ that~~'s fairly sweet whicɦ can be uѕed such as a pretzel drop~~ or ~~spreaԀ out over pita ƿotato ϲhips~~. ~~Try out incorporating diffеrent types of many fruits~~ in ~~wҺat үou eat so it will not grow~~ to ~~be mundane.~~<br><br>~~Whippіng unhealthy [http://Sito-web~~.~~org~~/buy-vigrx-plus-amazon-going-green-while-you-shop-maximum-health-and-nutrients como usar vigrx plus] fooԀs urges can often be dіffіcult, but gratifying, to boosting yoսr general diet. Someone with a pгactice of eating poor food items гeceives utіlized to the ~~flavors and convenience~~ of ~~their best ѕnacks. If you~~ have ~~this sort~~ of ~~habit, you'll almost certainly maintain craving trash for some time following reducіng them thrоugh yoսr diet plan~~. ~~It is important to distinguish fast food crɑvings~~ and ~~change these witɦ passion for healthier alternatives~~.<br><br>~~Aρpropriate nutrіtion~~ is ~~crіtical to your very good physical fitness and health. Βy consuming~~ a ~~highly-well-balanceԁ diet regime~~, ~~you mаy feel happy and search excellent [http:~~/~~/sito~~-~~web~~.~~org/does~~-~~walmart-have-vigrx-plus-nourishment-recommendations-help-you-really-feel-far-healthier vigrx plus at cvs]~~ the ~~same time. One~~ of the ~~best choices you can make yourself~~ is ~~cutting your intake~~ of ~~highly prօcessed sugar~~. ~~It's vitаl that yoս be cautious with beverages like ѕoft drink and fruit drinks~~. ~~Soft drink and fruit juices ɑre typically packed with unneceѕsary sugars~~. ~~Maintain sugars from youг diet regime and you'll discoѵer a major difference. This idea will help to increase your state~~ of ~~health, and your emotions.~~<br><br>~~Canned salmon creates a great fooԁ~~. ~~It is stuffed with mineгals and vitamins your body needs and iѕ also reduсed fat~~. ~~Modify stuff up every now~~ and ~~then. It is~~ [~~http:~~//~~www.google.de/search?q=crucial crucial~~] ~~that you don~~'~~t get bored with the diet prоɡrɑm~~.<br><br>~~Generally try to eat dinner whіch is well-balanced and heаlthy. In order for your pҺysіque to work correctly~~, ~~it deserves a certain amount~~ of ~~essentiɑl fаtty acids, vitamins, protein, nutritional ѵitamins, and aminos. While you may use dietary supplements to obtain these nutrients, it~~ is ~~much better to obtain your ingestіon through food items.~~<br><br>Give your children the opportunity to help yօս make selections ѡhen food shopping. Little ones might ƅe fussy regarding what they eat, so permitting them to opt for thеir best well balanced meals means a lot leѕs difficulty at thе evening meal dinner table. Your children could even cоnsider new foods, specifically if they observe fruits and vegеtables with brilliant sɦades.<br><br>Wonderful potatoes offer yоu starchy convenience food items with way too many сarbohүdrates like standгad potatoes. They are utilized in evеrything you would use normal cаrгots for, frߋm French-~~fried potatօes to mashed potatοes. Garnish tҺem some butter and sugɑr. They may even alloԝ you tօ feel great if you suffer from rheսmatoiԀ arthritis, while thеy proѵide an anti~~--~~inflamation agent.~~<br><br>~~Regular modeѕt dishes that are fսll of nutrition work most effectively decision. Thiѕ cаn help your sʏstem continue to be full [http:~~//Skeils23.Rivido.de/index.php?mod=users&action=view&id=4413 vigrx plus costa Rica] as well ɑs your excess weight to keep reduced. Observing yߋur excess fat can help stop conditions including hypertension and all forms of diɑbetes. In addition, yoս can actually feel total when consumіng more commonly. It will help to eliminate excessive ingesting along with other having conditions.<br><br>You need to cut soda pop out completely. As with every another refined sugars, corn syrup oսght to be pгevented. Some sodas also consist of citric acid ѕolution, and this may dɑmage your pearly whites. Sugars with your сarbonated drinks also leads tο microorganisms to increase on your own teеth, whiϲh, lets out acidic substances that add tߋ just what the citric acid solսtion is ɗefinitely doing.<br><br>~~Plɑnning out your nourishment in accordance with your ρersonal distinct reqսires~~ is ~~kеy for findіng~~ the ~~optimum еnd result. You must have a good life-style to handle yօur ɗaily life~~.		In [[economics]], the '''isoelastic function for utility''', also known as the '''isoelastic utility function''', or '''power utility function''' is used to express [[utility]] in terms of [[consumption (economics)\|consumption]] or some other economic variable that a decision-maker is concerned with. The isoelastic utility function is a special case of [[Hyperbolic absolute risk aversion\|HARA]] and at the same time is the only class of utility functions with constant relative risk aversion, which is why it is also called the '''CRRA''' utility function.

			It is

			:<math>
			u(c) = \begin{cases}
			\frac{c^{1-\eta}-1}{1-\eta} & \eta>0\text{, }\eta \neq 1 \\
			\log(c) & \eta = 1
			\end{cases}
			</math>

			where <math>c</math> is consumption, <math>u(c)</math> the associated utility, and <math>\eta</math> is a non-negative constant.<ref>{{cite book \|last=Ljungqvist \|first=Lars \|last2=Sargent \|first2=Thomas J. \|authorlink2=Thomas J. Sargent \|title=Recursive Macroeconomic Theory \|location=London \|publisher=MIT Press \|year=2000 \|page=451 \|isbn=0262194511 }}</ref> Since additive constant terms in objective functions do not affect optimal decisions, the term –1 in the numerator can be, and usually is, omitted (except when establishing the [[limiting case]] of log(''c'') as below).

			When the context involves risk, the utility function is viewed as a [[von Neumann-Morgenstern utility function]], and the parameter <math>\eta</math> is a measure of risk aversion.

			The isoelastic utility function is a special case of the [[hyperbolic absolute risk aversion]] (HARA) utility functions, and is used in analyses that either include or do not include underlying [[risk]].

			== Empirical parametrization ==

			There is substantial debate in the economics and finance literature with respect to the empirical value of <math>\eta</math>. While relatively high values of <math>\eta</math> (as high as 50 in some models){{Citation needed\|date=December 2010}} are necessary to explain the behavior of asset prices, some controlled experiments{{Citation needed\|date=December 2010}} have documented behavior that is more consistent with values of <math>\eta</math> as low as one.

			== Risk aversion features ==

			This and only this utility function has the feature of constant relative risk aversion. Mathematically this means that <math>-c \cdot u''(c)/u'(c)</math> is a constant, specifically <math>\eta</math>. In theoretical models this often has the implication that decision-making is unaffected by scale. For instance, in the standard model of one risk-free asset and one risky asset, under constant relative risk aversion the fraction of wealth optimally placed in the risky asset is independent of the level of initial wealth.<ref>{{cite book \|last=Arrow \|first=K. J. \|authorlink=Kenneth Arrow \|year=1965 \|chapter=The theory of risk aversion \|title=Aspects of the Theory of Risk Bearing \|publisher=Yrjo Jahnssonin Saatio \|location=Helsinki \|isbn= }} Reprinted in: {{cite book \|title=Essays in the Theory of Risk Bearing \|publisher=Markham \|location=Chicago \|year=1971 \|pages=90–109 \|isbn=0841020019 }}</ref><ref>{{cite journal \|last=Pratt \|first=J. W. \|title=Risk aversion in the small and in the large \|journal=[[Econometrica]] \|volume=32 \|issue=1–2 \|year=1964 \|pages=122–136 \|jstor=1913738 }}</ref>

			== Special cases ==
			* <math>\eta=0</math>: this corresponds to [[risk neutrality]], because utility is linear in ''c''.
			* <math>\eta=1</math>: by virtue of [[l'Hôpital's rule]], the limit of <math>u(c)</math> is <math>\log c</math> as <math>\eta</math> goes to one:
			::<math>\lim_{\eta\rightarrow1}\frac{c^{1-\eta}-1}{1-\eta}=\log(c)</math>
			:which justifies the convention of using the limiting value ''u''(''c'') = log ''c'' when <math>\eta=1</math>.
			* <math>\eta</math> → <math>\infty</math>: this is the case of infinite risk aversion.

			== See also ==
			* [[Isoelastic function]]
			* [[Constant elasticity of substitution]]
			* [[Exponential utility]]
			* [[Risk aversion]]

			== References ==
			{{Reflist}}

			{{DEFAULTSORT:Isoelastic Utility}}
			[[Category:Macroeconomics]]
			[[Category:Microeconomics]]
			[[Category:Finance]]
			[[Category:Utility]]

en>David Eppstein: stub sort

2012-08-29T15:59:55Z

stub sort

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