1. Cost Functions and Utility-Based Market Makers
We wish to find the cost function that matches a given utility function.
Actually what we are trying to solve is:
For example, for the logarithmic utility function with b>0: ,the cost function for two outcome event is:
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)