Cost Functions and UtilityBased Market Makers
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We wish to find the cost function that matches a given utility
function.
Actually what we are trying to solve is:
pi CF  piUB 
C ( q )
u '(C ( q )  qi )
(*)

qi
 u '(C (q )  q j )
j
For example, for the logarithmic utility function with b>0:
(**) u(m)  log(b  m) ,the cost function for two outcome event is:
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(***)
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Verify it for homework – just show that substituting the derivatives
of (**) and (***) into (*) gives a correct equality.
This topic is addressed in part 5.2 of the paper (A Utility
Framework for Bounded-Loss Market Makers)