Actuarial Outpost > MFE relationship between Uh and Qh in context of utilities
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#1
02-15-2012, 06:06 AM
 Akwasi Member Join Date: Aug 2009 College: University of Ghana. 3rd year Posts: 49
relationship between Uh and Qh in context of utilities

Hello all, please can somebody explain to me the difference between Uh and Qh in the context of utility in section 5.2 in asm. I have read this for like six times but i am not getting it. Forgive me if you think this is trivial, but i really need somebody to explain this to me in the simplest of terms.
Also why is Qh = pUh and Qh + Ql = 1/(1+r).
#2
02-15-2012, 10:34 AM
 psu602 Member SOA Join Date: May 2009 Location: Florence, KY Studying for FAP College: Penn State Univerisity 2010 Favorite beer: Cheerwine Posts: 354

Quote:
 Originally Posted by Akwasi Hello all, please can somebody explain to me the difference between Uh and Qh in the context of utility in section 5.2 in asm. I have read this for like six times but i am not getting it. Forgive me if you think this is trivial, but i really need somebody to explain this to me in the simplest of terms. Also why is Qh = pUh and Qh + Ql = 1/(1+r). Thanks in advance.
U is the value of a dollar, in terms of Utility.

Utility theory says that a dollar gained is not as valuable as a dollar lost. To illustrate what Utility theory is, let's assume you make \$25k per year. Consider the following scenarios:

-Your salary increases by \$25k (to \$50k total)
-Your salary decreases by \$25k (to nothing)

The amount of "happiness" in scenario 1 is LESS dramatic than the amount of "unhappiness" in scenario 2. Insurance exists because of Utility Theory.

Back to your question, Q is the probability of receiving that dollar times it's value (in utility). U is just the value of it, with no probability involved.
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#3
02-15-2012, 11:05 AM
 mathmajor Member SOA Join Date: Dec 2010 Studying for DP Health College: B.S. Applied Math '09 Favorite beer: Crown 'n Coke Posts: 2,374

You really don't need to understand the "usefulness" idea to get Q vs. U.

Basically, U is the buying power of \$1 at the end of the year. Uh is the amount gained if the "H" state happens, and Ul is if the "L" state happens. Qh is the present value of prob(H)*Uh. Qh can be thought of as Uh's contribution to the PV of the expected value. Added together, these should add to the present value of \$1, or 1/(1+r).
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#4
02-15-2012, 11:16 AM
 actuary_aspire Member CAS Join Date: Sep 2009 Studying for OC1 Posts: 2,231

Quote:
 Originally Posted by mathmajor You really don't need to understand the "usefulness" idea to get Q vs. U. Basically, U is the buying power of \$1 at the end of the year. Uh is the amount gained if the "H" state happens, and Ul is if the "L" state happens. Qh is the present value of prob(H)*Uh. Qh can be thought of as Uh's contribution to the PV of the expected value. Added together, these should add to the present value of \$1, or 1/(1+r).
Uh is the utility now of getting 1\$ in the up state, so Qh is just prob(H)*Uh.

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