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For example: The utility function is ln(W), where W refers to the Wealth level. The initial wealth is $10,000 $ and you have a equal chance of winning and losing $1000.

What if the insurance policy only covers the loss, how are you willing to pay for the insurance premium?

Need some guidance on solving this question.

lakshmen
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1 Answers1

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So you end up with either $10000-p$ or $11000-p$ instead of either $9000$ or $11000$. You must solve for $p$ in $$\frac 12\ln(10000-p)+\frac12\ln(11000-p) = \frac12\ln 9000+\frac12\ln 11000$$ or equivalently $$ (10000-p)(11000-p)=9000\cdot 11000$$ whihc is a quadratic in $p$ where one of the roots is between $0$ and $1000$ (and the other makes both factors on the left negative and can be ignored). It turns out that the premium will eat more than half of your hoped-for profit ...

Hagen von Eitzen
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  • I understand the quadratic eqn part but why do you equate the expected utility with insurance to expected utility without insurance? – lakshmen Aug 05 '13 at 06:57
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    @lakesh in expected utility theory, the rational decision maker will make the decision by attempting to maximize the expected value of utility under different scenarios. By equating the expected utility w/ and w/o insurance, one find the breakeven point where the rational decision maker will accept or decline the insurance. – achille hui Aug 05 '13 at 07:46