Exchange interaction - Revision history

en>Dexbot: Removing Link GA template (handled by wikidata)

2014-09-03T15:55:58Z

Removing Link GA template (handled by wikidata)

← Older revision		Revision as of 17:55, 3 September 2014
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	~~Irwin Butts~~ is ~~what my wife loves to contact me though I don't truly like being known as like that~~. ~~For a whilst she~~'s been ~~in at home std test South Dakota. [http://xrambo.com/user/RKDBG Suggested Website] The [http://Www.Trichomoniasis.org/ favorite pastime]~~ for ~~my children~~ and me is ~~to perform [http://livestudentjobs~~.~~co.uk/groups/solid-advice-for-handling-a-candida/ livestudentjobs.co.uk] baseball but I haven't made a dime with it. He used to be unemployed but now he at home std testing~~ is ~~a pc std testing at home operator but his marketing by no means comes~~.<br><br>~~my web blog -~~ [http://~~biztoc~~.com/~~mod~~/~~groups/topicposts~~.~~php?topic=1311479&group_guid=1311468 over the counter std test~~]		Nice to meet you, my name is Refugia. Puerto Rico is where he's been living for many years and he will never move. Managing people is his profession. Doing ceramics is what her family and her appreciate.<br><br>My site; [http://www.hard-ass-porn.com/blog/111007 www.hard-ass-porn.com]

130.237.25.175 at 16:00, 4 March 2014

2014-03-04T16:00:12Z

← Older revision		Revision as of 18:00, 4 March 2014
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	~~{{Unreferenced\|date=December 2009}}~~		Irwin Butts is what my wife loves to contact me though I don't truly like being known as like that. For a whilst she's been in at home std test South Dakota. [http://xrambo.com/user/RKDBG Suggested Website] The [http://Www.Trichomoniasis.org/ favorite pastime] for my children and me is to perform [http://livestudentjobs.co.uk/groups/solid-advice-for-handling-a-candida/ livestudentjobs.co.uk] baseball but I haven't made a dime with it. He used to be unemployed but now he at home std testing is a pc std testing at home operator but his marketing by no means comes.<br><br>my web blog - [http://biztoc.com/mod/groups/topicposts.php?topic=1311479&group_guid=1311468 over the counter std test]
	~~An '''actuarial reserve'''~~ is ~~a liability equal~~ to ~~the [[net present value]] of the future expected cash flows of~~ a ~~contingent event~~. In the insurance context an actuarial reserve is the present value of the future cash flows of an insurance policy and the total liability of the insurer is the sum of the actuarial reserves for every individual policy. Regulated insurers are required to keep offsetting assets to pay off this future liability.

	~~==The Loss Random Variable==~~
	~~The loss~~ [~~[random variable]] is the starting point in the determination of any type of actuarial reserve calculation. Define <math>K(x)<~~/~~math> to be the future state lifetime random variable of a person aged x~~. ~~Then, for a death benefit of one dollar and premium <math>P<~~/~~math>, the loss random variable, <math>L<~~/~~math>, can be written in~~ [~~[actuarial notation]] as a function of <math>K(x)<~~/~~math>~~

	~~:<math> L = v^{K(x)+1} - P\ddot{a}_{\overline{K(x)+1}\|}<~~/~~math>~~

	From this we can see that the present value of the loss to the insurance company now if the person dies in t years, is equal to the present value of the death benefit minus the present value of the premiums.

	~~The loss random variable described above only defines the loss at issue~~. ~~For K(x)>t, the loss random variable at time t can be defined as:~~

	~~:<math> {}_{t}L = v^{K(x)+1-t} - P\ddot{a}_{\overline{K(x)+1-t\|}}<~~/~~math>~~

	~~==Net Level Premium Reserves==~~
	~~Net level premium reserves, also called benefit reserves, only involve two cash flows and are used for some [[Generally Accepted Accounting Principles (USA)\|US GAAP~~]] reporting purposes. The valuation premium in an NLP reserve is a premium such that the value of the reserve at time zero is equal to zero. The net level premium reserve is found by taking the expected value of the loss random variable defined above. They can be formulated prospectively or retrospectively. The amount of prospective reserves at a point in time is derived by subtracting the [[actuarial present value]] of future valuation premiums from the actuarial present value of the future insurance benefits. Retrospective reserving subtracts accumulated value of benefits from accumulated value of valuation premiums as of a point in time. The two methods yield identical results (assuming bases are the same for ~~both prospective~~ and ~~retrospective calculations).~~

	As an example, consider a whole life insurance policy of one dollar issues on (x) with yearly premiums paid at the start of the year and death benefit paid at the end of the year. In actuarial notation, a benefit reserve is denoted as ''V''. Our objective is to ~~find the value of the net level premium reserve at time t~~. ~~First we define the loss random variable at time zero for this policy~~. ~~Hence~~

	~~:<math>L = v^{K(x)+1} - P\ddot{a}_{\overline{K(x)+1\|}}<~~/~~math>~~
	~~Then, taking expected values we have:~~
	~~:<math>\operatorname{E}[L] = \operatorname{E}[v^{K(x)+1} - P\ddot{a}_{\overline{K(x)+1\|}}]<~~/~~math>~~

	~~:<math>\operatorname{E}[L] = \operatorname{E}[v^{K(x)+1}]~~ - ~~P\operatorname{E}[\ddot{a}_{\overline{K(x)+1\|}}]</math>~~

	~~:<math>{}_0\!V_x=A_{x}~~-~~P\cdot\ddot{a}_{x}</math>~~

	~~Setting the reserve equal to zero and solving~~ for ~~P yields:~~

	~~:<math>P=\frac{A_{x}}{\ddot{a}_{x}}</math>~~
	~~For a whole life policy as defined above the premium is denoted as <math>P_{x}</math> in actuarial notation.~~
	~~The NLP reserve at time t is the expected value of the loss random variable at time t given K(x)>t~~

	~~:<math> {}_{t}L = v^{K(x)+1~~-t} - ~~P_{x}\ddot{~~a~~}_{\overline{K(x)+1~~-~~t\|}}<~~/~~math>~~
	~~:<math> \operatorname{E}[{}_{t}L\|K(x)>t~~] ~~= \operatorname{E}[v^{K(x)+1-t}\|K(x)>t] - P_{x}\operatorname{E}[\ddot{a}_{\overline{K(x)+1-t\|}}\|K(x)>~~t~~]</math>~~

	~~:<math>{}_t\!V_x=A_{x+t}-P_x\cdot\ddot{~~a~~}_{x+t}</math> Where <math>{ }P_x=\frac{A_{x}}{\ddot{a}_{x}}</math>~~

	~~==Computation of actuarial reserves==~~
	~~The calculation process often involves a number of assumptions, particularly in relation~~ to ~~future claims experience, and investment earnings potential.~~ Generally, the computation involves calculating the expected claims for each future time period. These expected future cash outflows are then discounted to reflect interest to the date of the expected cash flow.

	~~For example, if we expect to pay $300,000 in Year 1, $200,000 in year 2 and $150,000 in Year 3, and we are able to invest reserves to earn 8%p.~~a~~., the respective contributions to Actuarial Reserves are:~~

	*Year 1: ~~$300,000 x (1~~.~~08)~~<~~sup~~>−1<~~/sup~~> ~~= $277,777.78~~
	*Year 2: ~~$200,000 x (1~~.~~08)<sup>−2<~~/~~sup>~~ = ~~$171,467.76~~
	*Year 3: $150,000 x (1.08)<sup>−3</sup> = ~~$119,074.84.~~

	~~If we sum the discounted expected claims~~ over ~~all years in which a claim could be experienced, we have completed~~ the ~~computation of Actuarial Reserves. In the above example, if there were no expected future claims after year 3, our computation would give Actuarial Reserves of $568,320.38.~~

	~~==See also==~~
	* [[Actuarial science]]
	* [[Actuary]]
	* [[Force of mortality]]
	* [[Life insurance]]
	* [[Life table]]
	* [[Statutory reserve]]

	~~{{DEFAULTSORT:Actuarial Reserves}}~~
	~~[[Category:Actuarial science]]~~

	~~[[de:Deckungsrückstellung]~~]

en>Quondum: Bose-Einstein condensation → Bose–Einstein condensation (hyphen → en-dash)

2013-11-25T19:13:00Z

Bose-Einstein condensation → Bose–Einstein condensation (hyphen → en-dash)

← Older revision		Revision as of 21:13, 25 November 2013
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	~~They call me Emilia~~. ~~Puerto Rico~~ is ~~where he's always been living but she needs~~ to ~~move simply because~~ of ~~her family members~~. ~~Hiring~~ is ~~her working day job now~~ and ~~she will not change it whenever quickly~~. ~~To collect coins~~ is one of the ~~issues I adore most~~.<br><br>~~Also visit my site~~: [~~http~~://~~www~~.~~ubi~~-~~cation.com~~/~~ubication~~/~~node/6056 http~~://~~www~~.~~ubi-cation~~.~~com~~/~~ubication~~/~~node~~/~~6056~~]		{{Unreferenced\|date=December 2009}}
			An '''actuarial reserve''' is a liability equal to the [[net present value]] of the future expected cash flows of a contingent event. In the insurance context an actuarial reserve is the present value of the future cash flows of an insurance policy and the total liability of the insurer is the sum of the actuarial reserves for every individual policy. Regulated insurers are required to keep offsetting assets to pay off this future liability.

			==The Loss Random Variable==
			The loss [[random variable]] is the starting point in the determination of any type of actuarial reserve calculation. Define <math>K(x)</math> to be the future state lifetime random variable of a person aged x. Then, for a death benefit of one dollar and premium <math>P</math>, the loss random variable, <math>L</math>, can be written in [[actuarial notation]] as a function of <math>K(x)</math>

			:<math> L = v^{K(x)+1} - P\ddot{a}_{\overline{K(x)+1}\|}</math>

			From this we can see that the present value of the loss to the insurance company now if the person dies in t years, is equal to the present value of the death benefit minus the present value of the premiums.

			The loss random variable described above only defines the loss at issue. For K(x)>t, the loss random variable at time t can be defined as:

			:<math> {}_{t}L = v^{K(x)+1-t} - P\ddot{a}_{\overline{K(x)+1-t\|}}</math>

			==Net Level Premium Reserves==
			Net level premium reserves, also called benefit reserves, only involve two cash flows and are used for some [[Generally Accepted Accounting Principles (USA)\|US GAAP]] reporting purposes. The valuation premium in an NLP reserve is a premium such that the value of the reserve at time zero is equal to zero. The net level premium reserve is found by taking the expected value of the loss random variable defined above. They can be formulated prospectively or retrospectively. The amount of prospective reserves at a point in time is derived by subtracting the [[actuarial present value]] of future valuation premiums from the actuarial present value of the future insurance benefits. Retrospective reserving subtracts accumulated value of benefits from accumulated value of valuation premiums as of a point in time. The two methods yield identical results (assuming bases are the same for both prospective and retrospective calculations).

			As an example, consider a whole life insurance policy of one dollar issues on (x) with yearly premiums paid at the start of the year and death benefit paid at the end of the year. In actuarial notation, a benefit reserve is denoted as ''V''. Our objective is to find the value of the net level premium reserve at time t. First we define the loss random variable at time zero for this policy. Hence

			:<math>L = v^{K(x)+1} - P\ddot{a}_{\overline{K(x)+1\|}}</math>
			Then, taking expected values we have:
			:<math>\operatorname{E}[L] = \operatorname{E}[v^{K(x)+1} - P\ddot{a}_{\overline{K(x)+1\|}}]</math>

			:<math>\operatorname{E}[L] = \operatorname{E}[v^{K(x)+1}] - P\operatorname{E}[\ddot{a}_{\overline{K(x)+1\|}}]</math>

			:<math>{}_0\!V_x=A_{x}-P\cdot\ddot{a}_{x}</math>

			Setting the reserve equal to zero and solving for P yields:

			:<math>P=\frac{A_{x}}{\ddot{a}_{x}}</math>
			For a whole life policy as defined above the premium is denoted as <math>P_{x}</math> in actuarial notation.
			The NLP reserve at time t is the expected value of the loss random variable at time t given K(x)>t

			:<math> {}_{t}L = v^{K(x)+1-t} - P_{x}\ddot{a}_{\overline{K(x)+1-t\|}}</math>
			:<math> \operatorname{E}[{}_{t}L\|K(x)>t] = \operatorname{E}[v^{K(x)+1-t}\|K(x)>t] - P_{x}\operatorname{E}[\ddot{a}_{\overline{K(x)+1-t\|}}\|K(x)>t]</math>

			:<math>{}_t\!V_x=A_{x+t}-P_x\cdot\ddot{a}_{x+t}</math> Where <math>{ }P_x=\frac{A_{x}}{\ddot{a}_{x}}</math>

			==Computation of actuarial reserves==
			The calculation process often involves a number of assumptions, particularly in relation to future claims experience, and investment earnings potential. Generally, the computation involves calculating the expected claims for each future time period. These expected future cash outflows are then discounted to reflect interest to the date of the expected cash flow.

			For example, if we expect to pay $300,000 in Year 1, $200,000 in year 2 and $150,000 in Year 3, and we are able to invest reserves to earn 8%p.a., the respective contributions to Actuarial Reserves are:

			*Year 1: $300,000 x (1.08)<sup>−1</sup> = $277,777.78
			*Year 2: $200,000 x (1.08)<sup>−2</sup> = $171,467.76
			*Year 3: $150,000 x (1.08)<sup>−3</sup> = $119,074.84.

			If we sum the discounted expected claims over all years in which a claim could be experienced, we have completed the computation of Actuarial Reserves. In the above example, if there were no expected future claims after year 3, our computation would give Actuarial Reserves of $568,320.38.

			==See also==
			* [[Actuarial science]]
			* [[Actuary]]
			* [[Force of mortality]]
			* [[Life insurance]]
			* [[Life table]]
			* [[Statutory reserve]]

			{{DEFAULTSORT:Actuarial Reserves}}
			[[Category:Actuarial science]]

			[[de:Deckungsrückstellung]]

134.94.14.29: added link to lecture notes

2012-08-21T07:00:08Z

added link to lecture notes

New page

They call me Emilia. Puerto Rico is where he's always been living but she needs to move simply because of her family members. Hiring is her working day job now and she will not change it whenever quickly. To collect coins is one of the issues I adore most.<br><br>Also visit my site: [http://www.ubi-cation.com/ubication/node/6056 http://www.ubi-cation.com/ubication/node/6056]