en>DerBorg: fix file link, moved as requested

2014-06-07T12:44:47Z

fix file link, moved as requested

← Older revision		Revision as of 14:44, 7 June 2014
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	~~{{refimprove\|date=April 2012}}~~		Home improvement can be done by nearly anyone for nearly any reason. Some are tired of the old look. Others hope to make money by increasing the value of their house. Some people get great enjoyment out of physical labor. Whatever your reason, here are some tips about home improvement.<br><br>Before allowing any contractor to start working have a signed contract. If you are undertaking an expensive home improvement project, it might be worth it to spend about $150 to have a lawyer review your home improvement contract before signing it. You should put in when the work will be finished, any guarantees on work, and what is going to be done.<br><br>Use old two-liter bottles for storage in your kitchen. You can use these to protect any dry goods like flour, sugar or corn meal. You can keep them in the freezer, on your shelf or in the refrigerator. With two-liter bottles all it takes is a simple twist of the cap to gain access to your products.<br><br>Make sure you shop around to find good deals on anything you need for your home improvement project. Getting new floors can be expensive, and when you compare prices you get a good deal. Shop at discount home supply stores and find stores that offer bargains.<br><br>Do not underestimate the amount of effort that your project will require. Create a list of all the tasks you must take care of. It is also smart to have a second opinion; you might have missed something in your initial assessment. By knowing everything you have to do, you can save tons of money.<br><br>Ask your family members and friends for help before you start your next project to improve your home. But try to find this help earlier rather than later. No one wants to come in when everything's a mess to try and help you. It might take you quite a while to finish up, which may put additional pressure on you to get it done.<br><br>When you have to buy bricks, always buy more than you require. It can be very difficult to find matching pieces at a later date when repairs need to be done. The style of bricks changes frequently. As the house ages, a reasonable supply of replacement bricks that match the original can be extremely helpful.<br><br>Try something different rather than a simple pre-made coffee table. An old trunk or chest look great in the center of a living room and provide storage, also. Toss a few coffee table books on it to imbue added flair. If you want a country style, add a tablecloth and a tea set.<br><br>It is very important that the contractor estimates you get are all based on the exact same work to be done. Be clear about what you want to replace or repair, and keep your request the same for every contractor you speak to. If you make changes, and get different estimates, you won't be comparing the same thing.<br><br>Install peepholes in your exterior doors. Know who's out there when you open your door. Anyone can afford and install a peephole thanks to their low cost and ease of installation. This project requires minimal time and tools. If you put one in, you will know who is at your door when you hear knocking.<br><br>If you need space, consider an addition. Consider the benefit of having more space for your family and your favorite activities. This will increase the comfort of your Should you have just about any inquiries regarding where in addition to the best way to employ home improvement diy ideas ([http://www.homeimprovementdaily.com just click the up coming document]), you can e mail us from our web site. home as well as the value of your home. You should of course do this project when you have accumulated the money.<br><br>If you would like to take on a home improvement project, there are many things you need to be aware of before you begin. There is a lot of preparation, understanding and planning that you are going to need to do, though you have to start with what is important to the project that you are going to be doing. Use these tips as a starting point for your next major home improvement project.

	~~The '''Snell envelope''', used in [[stochastics]] and [[mathematical finance]], is~~ the ~~smallest [[Martingale (probability theory)\|supermartingale]] dominating a [[stochastic process]]~~. ~~The Snell envelope is named after [[James Laurie Snell]]~~.

	~~== Definition ==~~
	~~Given a [[filtered probability space]] <math>(\Omega~~,~~\mathcal{F},(\mathcal{F}_t)_{t \in [0,T]},\mathbb{P})</math> and an [[absolutely continuous]] [[probability measure]]~~ <~~math~~>~~\mathbb{Q} \ll \mathbb{P}~~<~~/math~~> ~~then~~ an ~~[[adapted process]] <math>U = (U_t)_{t \~~in [0,~~T]}</math>~~ is ~~the Snell envelope with respect~~ to <~~math~~>~~\mathbb{Q}~~<~~/math~~> of the ~~process <math>X = (X_t)_{t \~~in ~~[0,T]}</math> if~~
	~~# <math>U</math>~~ is a <~~math~~>~~\mathbb{Q}~~<~~/math>-supermartingale~~
	~~# <math>U</math> dominates <math>X</math~~>, i.e. <~~math~~>~~U_t \geq X_t~~<~~/math~~> ~~<math>\mathbb{Q}</math>-[[almost surely]] for~~ all ~~times <math>t \~~in [0,T]<~~/math~~>
	~~# If~~ <~~math~~>~~V = (V_t)_{t \~~in [0,~~T]}</math> is a <math>\mathbb{Q}</math>-supermartingale~~ which ~~dominates~~ <~~math~~>X<~~/math~~>, ~~then~~ <~~math~~>V<~~/math> dominates <math>U</math~~>.~~<ref name="FollmerSchied">{{cite book\|first1=Hans\|last1=Föllmer\|first2=Alexander\|last2=Schied\|title=Stochastic finance: an introduction~~ in ~~discrete time\|publisher=Walter de Gruyter\|year=2004\|edition=2\|isbn=9783110183467\|pages=280-282}}</ref>~~

	~~== Construction ==~~
	~~Given~~ a ~~(discrete) [[filtered probability space]] <math>(\Omega~~,~~\mathcal{F}~~,~~(\mathcal{F}_n)_{n = 0}^N,\mathbb{P})</math>~~ and ~~an [[Absolutely continuous#Absolute continuity of measures\|absolutely continuous]] [[probability measure]]~~ <~~math~~>~~\mathbb{Q} \ll \mathbb{P}~~<~~/math~~> ~~then~~ the ~~Snell envelope~~ <~~math~~>~~(U_n)_{n = 0}^N~~<~~/math~~> ~~with respect~~ to <~~math~~>~~\mathbb{Q}~~<~~/math~~> of the ~~process <math>~~(~~X_n)_{n = 0}^N<~~/~~math> is given by~~ the ~~recursive scheme~~
	~~:<math>U_N := X_N,</math>~~
	~~:<math>U_n := X_n \lor \mathbb{E}^{\mathbb{Q}}[U_{n+1} \mid \mathcal{F}_n~~]~~</math> for <math>n = N-1~~,...~~,0</math>~~
	~~where~~ <~~math~~>~~\lor~~<~~/math~~> ~~is the [[join and meet\|join]]~~.~~<ref name="FollmerSchied" />~~

	~~== Application ==~~
	* If <math>X</math> is a ~~discounted [[American option]] payoff~~ with ~~Snell envelope <math>U</math> then <math>U_t</math>~~ is the ~~minimal capital requirement~~ to ~~hedge <math>X</math> from time <math>t</math> to the expiration date~~.~~<ref name="FollmerSchied" />~~

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

	~~[[Category:Mathematical finance]]~~

69.91.186.162: /* Neosubfunctionlization */

2014-01-20T22:01:11Z

Neosubfunctionlization

← Older revision		Revision as of 00:01, 21 January 2014
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	~~Hello~~, ~~I'm Lieselotte~~, a ~~24 year old from East Wittering, United Kingdom~~.<br>~~My hobbies include~~ (~~but are not limited to~~) ~~Element collecting~~, ~~Backpacking~~ and ~~watching Game~~ of ~~Thrones~~.<br><br>~~Also visit my webpage home improvement diy ideas~~ - [~~http~~://~~www~~.~~homeimprovementdaily~~.~~com discover here~~],		{{refimprove\|date=April 2012}}

			The '''Snell envelope''', used in [[stochastics]] and [[mathematical finance]], is the smallest [[Martingale (probability theory)\|supermartingale]] dominating a [[stochastic process]]. The Snell envelope is named after [[James Laurie Snell]].

			== Definition ==
			Given a [[filtered probability space]] <math>(\Omega,\mathcal{F},(\mathcal{F}_t)_{t \in [0,T]},\mathbb{P})</math> and an [[absolutely continuous]] [[probability measure]] <math>\mathbb{Q} \ll \mathbb{P}</math> then an [[adapted process]] <math>U = (U_t)_{t \in [0,T]}</math> is the Snell envelope with respect to <math>\mathbb{Q}</math> of the process <math>X = (X_t)_{t \in [0,T]}</math> if
			# <math>U</math> is a <math>\mathbb{Q}</math>-supermartingale
			# <math>U</math> dominates <math>X</math>, i.e. <math>U_t \geq X_t</math> <math>\mathbb{Q}</math>-[[almost surely]] for all times <math>t \in [0,T]</math>
			# If <math>V = (V_t)_{t \in [0,T]}</math> is a <math>\mathbb{Q}</math>-supermartingale which dominates <math>X</math>, then <math>V</math> dominates <math>U</math>.<ref name="FollmerSchied">{{cite book\|first1=Hans\|last1=Föllmer\|first2=Alexander\|last2=Schied\|title=Stochastic finance: an introduction in discrete time\|publisher=Walter de Gruyter\|year=2004\|edition=2\|isbn=9783110183467\|pages=280-282}}</ref>

			== Construction ==
			Given a (discrete) [[filtered probability space]] <math>(\Omega,\mathcal{F},(\mathcal{F}_n)_{n = 0}^N,\mathbb{P})</math> and an [[Absolutely continuous#Absolute continuity of measures\|absolutely continuous]] [[probability measure]] <math>\mathbb{Q} \ll \mathbb{P}</math> then the Snell envelope <math>(U_n)_{n = 0}^N</math> with respect to <math>\mathbb{Q}</math> of the process <math>(X_n)_{n = 0}^N</math> is given by the recursive scheme
			:<math>U_N := X_N,</math>
			:<math>U_n := X_n \lor \mathbb{E}^{\mathbb{Q}}[U_{n+1} \mid \mathcal{F}_n]</math> for <math>n = N-1,...,0</math>
			where <math>\lor</math> is the [[join and meet\|join]].<ref name="FollmerSchied" />

			== Application ==
			* If <math>X</math> is a discounted [[American option]] payoff with Snell envelope <math>U</math> then <math>U_t</math> is the minimal capital requirement to hedge <math>X</math> from time <math>t</math> to the expiration date.<ref name="FollmerSchied" />

			== References ==
			{{Reflist}}

			[[Category:Mathematical finance]]

en>Sun Creator: Typo fixing and General, typos fixed: the exact same → exactly the same using AWB

2012-05-26T22:36:54Z

Typo fixing and General, typos fixed: the exact same → exactly the same using AWB

New page

Hello, I'm Lieselotte, a 24 year old from East Wittering, United Kingdom.<br>My hobbies include (but are not limited to) Element collecting, Backpacking and watching Game of Thrones.<br><br>Also visit my webpage home improvement diy ideas - [http://www.homeimprovementdaily.com discover here],

Neofunctionalization - Revision history

en>DerBorg: fix file link, moved as requested

69.91.186.162: /* Neosubfunctionlization */

en>Sun Creator: Typo fixing and General, typos fixed: the exact same → exactly the same using AWB