Uncertainty and Risk - DARP
Uncertainty and Risk - DARP
Uncertainty and Risk - DARP
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Microeconomics CHAPTER 8. UNCERTAINTY AND RISK<br />
Exercise 8.6 An example to illustrate regret. Let<br />
P := f(x ! ; ! ) : ! 2 g<br />
P 0 := f(x 0 !; ! ) : ! 2 g<br />
be two prospects available to an individual. De…ne the expected regret if the<br />
person chooses P rather than P 0 as<br />
X<br />
! max fx 0 ! x ! ; 0g (8.1)<br />
!2<br />
Now consider the choices amongst prospects presented in Exercise 8.4. Show<br />
that if a person is concerned to minimise expected regret as measured by (8.1),<br />
then it is reasonable that the person select P 2 when P 1 is also available <strong>and</strong> then<br />
also select P 4 when P 3 is available.<br />
Outline Answer:<br />
Denote the regret in (8.1) by r (P; P 0 ).<br />
If I choose P 2 when P 1 is also available then the regret is<br />
r (P 2 ; P 1 ) = 0:1 [0] + 0:89 [0] + :01 [1]<br />
= 10; 000<br />
Whereas, had I chosen P 1 when P 2 was available, then the regret would have<br />
been<br />
r (P 1 ; P 2 ) = 0:1 [4; 000; 000] + 0:89 [0] + :01 [0]<br />
= 400; 000<br />
If I choose P 4 when P 3 is also available then the regret is<br />
r (P 4 ; P 3 ) = 0:1 [0] + 0:89 [0] + :01 [0]<br />
= 0<br />
Whereas, had I chosen P 3 when P 4 was available, then the regret would have<br />
been<br />
r (P 3 ; P 4 ) = 0:1 [0] + 0:89 [0] + :01 [5; 000; 000]<br />
= 50; 000<br />
cFrank Cowell 2006 120