Denotational semantics of the Actor model - Revision history

en>Rosiestep: /* Denotations */ wl

2014-04-19T23:56:08Z

Denotations: wl

← Older revision		Revision as of 01:56, 20 April 2014
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	~~==Nominal return==~~		Jayson Berryhill is how I'm called and my spouse doesn't like it at all. For a whilst I've been in Alaska but I will have to move in a yr or two. She is truly fond of caving but she doesn't have the time recently. He is an information officer.<br><br>My weblog :: [http://www.herandkingscounty.com/content/information-and-facts-you-must-know-about-hobbies telephone psychic]
	~~Let ''P''<sub>''t''</sub> be the price of a security at time '~~'~~t'', including any cash dividends or [[interest]],~~ and ~~let ''P''<sub>'~~'t~~'' − 1</sub> be its price~~ at ~~''t'' − 1~~. ~~Let~~ '~~'RS''<sub>''t''</sub> be the simple rate of return on the security from ''t'' − 1~~ to ~~''t''. Then~~

	~~: <math> 1 + RS_{t}=\frac{P_{t}}{P_{t-1}}.</math>~~

	~~The '''continuously compounded rate of return'''~~ or ~~'''instantaneous rate of return''' ''RC<sub>t</sub>'' obtained during that period is~~

	~~: <math> RC_{t}=\ln\left (\frac{P_{t}}{P_{t-1}}\right )~~.~~</math>~~

	~~If this instantaneous return~~ is received continuously for one period, then the initial value ''P''<sub>''t-1''</sub> will grow to <math>P_t = P_{t-1} \cdot e^{RC_t}</math> during that period. See also [[Compound interest\|continuous compounding]].

	~~Since this analysis did not adjust for the effects~~ of ~~[[inflation]] on the purchasing power of ''P''<sub>''t''</sub>, ''RS'' and~~ '~~'RC'' are referred to as [[Real versus nominal value (economics)\|nominal rates of return]].~~

	~~==Real return==~~
	~~Let <math> \pi _~~ t~~</math> be~~ the ~~purchasing power of a dollar at~~ time ~~''t'' (the number of bundles of consumption that can be purchased for $1)~~. ~~Then <math>\pi_t = 1/(PL_t)</math>, where ''PL''<sub>''t''</sub>~~ is ~~the price level at ''t'' (the dollar price of a bundle of consumption goods)~~. ~~The simple inflation rate ''IS''~~<~~sub~~>~~''t''~~<~~/sub> from ''t'' –1 to ''t'' is <math>\tfrac {PL_t}{PL_{t-1}} - 1</math~~>~~. Thus, continuing the above nominal example, the final value of the investment expressed in [[Real versus nominal value (economics)\|real]] terms is~~

	:~~<math>P_t^{real} = P_t \cdot \frac{PL_{t-1}}{PL_t}.</math>~~

	~~Then the continuously compounded real rate of return <math>RC^{real}</math> is~~

	: ~~<math> RC_{t}^{real}=\ln\left (\frac{P_{t}^{real}}{P_{t-1}}\right ).</math>~~

	~~The continuously compounded real rate of return is just the continuously compounded nominal rate of return minus the continuously compounded inflation rate.~~

	~~==Source==~~
	*[http://~~gsbwww~~.~~uchicago~~.~~edu~~/~~fac~~/~~eugene.fama/teaching/Reading%20List%20and%20Notes/Continuously%20Componded%20Returns.doc Eugene Fama Notes]~~

	~~{{DEFAULTSORT:Continuously Compounded Nominal And Real Returns}}~~
	~~[[Category:Applied mathematics]~~]

en>Nirakka: /* Other programming language constructs */ typo

2013-06-04T16:35:53Z

Other programming language constructs: typo

← Older revision		Revision as of 18:35, 4 June 2013
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	~~Alyson is what my spouse loves to contact me but I don~~'t ~~like when individuals use my full title~~. ~~For many years she~~'~~s been residing in Kentucky but her husband desires them~~ to ~~move~~. ~~To climb~~ is ~~some thing I really enjoy doing~~. ~~Office supervising~~ is ~~my profession~~.<br><br>~~Also visit my blog; psychic love readings~~ (~~[http:~~//~~checkmates~~.~~co.za~~/~~index~~.~~php?do~~=/~~profile~~-~~56347/info~~/ http://~~checkmates~~.co.za/~~index~~.~~php?do=~~/~~profile-56347~~/~~info~~/])		==Nominal return==
			Let ''P''<sub>''t''</sub> be the price of a security at time ''t'', including any cash dividends or [[interest]], and let ''P''<sub>''t'' − 1</sub> be its price at ''t'' − 1. Let ''RS''<sub>''t''</sub> be the simple rate of return on the security from ''t'' − 1 to ''t''. Then

			: <math> 1 + RS_{t}=\frac{P_{t}}{P_{t-1}}.</math>

			The '''continuously compounded rate of return''' or '''instantaneous rate of return''' ''RC<sub>t</sub>'' obtained during that period is

			: <math> RC_{t}=\ln\left (\frac{P_{t}}{P_{t-1}}\right ).</math>

			If this instantaneous return is received continuously for one period, then the initial value ''P''<sub>''t-1''</sub> will grow to <math>P_t = P_{t-1} \cdot e^{RC_t}</math> during that period. See also [[Compound interest\|continuous compounding]].

			Since this analysis did not adjust for the effects of [[inflation]] on the purchasing power of ''P''<sub>''t''</sub>, ''RS'' and ''RC'' are referred to as [[Real versus nominal value (economics)\|nominal rates of return]].

			==Real return==
			Let <math> \pi _ t</math> be the purchasing power of a dollar at time ''t'' (the number of bundles of consumption that can be purchased for $1). Then <math>\pi_t = 1/(PL_t)</math>, where ''PL''<sub>''t''</sub> is the price level at ''t'' (the dollar price of a bundle of consumption goods). The simple inflation rate ''IS''<sub>''t''</sub> from ''t'' –1 to ''t'' is <math>\tfrac {PL_t}{PL_{t-1}} - 1</math>. Thus, continuing the above nominal example, the final value of the investment expressed in [[Real versus nominal value (economics)\|real]] terms is

			:<math>P_t^{real} = P_t \cdot \frac{PL_{t-1}}{PL_t}.</math>

			Then the continuously compounded real rate of return <math>RC^{real}</math> is

			: <math> RC_{t}^{real}=\ln\left (\frac{P_{t}^{real}}{P_{t-1}}\right ).</math>

			The continuously compounded real rate of return is just the continuously compounded nominal rate of return minus the continuously compounded inflation rate.

			==Source==
			*[http://gsbwww.uchicago.edu/fac/eugene.fama/teaching/Reading%20List%20and%20Notes/Continuously%20Componded%20Returns.doc Eugene Fama Notes]

			{{DEFAULTSORT:Continuously Compounded Nominal And Real Returns}}
			[[Category:Applied mathematics]]

en>David Eppstein: /* The domain of Actor computations */ change wikilink

2012-08-15T18:00:46Z

The domain of Actor computations: change wikilink

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