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Is it possible to infer investor's utility function from the set of decisions she is making?
Let's assume for simplicity that the market consists of a single traded asset whose return distribution is stationary and known to the agents. We are also given a set of trades made by a particular investor in this market. We also know the wealth of an investor. How do we estimate the investor's utility function from this data?
The problem is to find the best functional form of the utility function plus estimate its parameters.
A good starting point is the following draft chapter from an upcoming book which gives a good intuition and many examples: Preferences by Andrew Ang
Yes, this has been done by Hackethal, Meyer and Jakusch.
If you have a single traded asset or a set of trades from traders, you could use those stated decisions to infer the form of the utility functions first and then find the risk parameters once you identified the utility function.
There is a bunch of papers from some these guys who just did that.
This paper is on a utility model selection approach: https://papers.ssrn.com/sol3/papers.cfm?abstract_id=2845866
This one on finding the correct risk parameters: https://papers.ssrn.com/sol3/papers.cfm?abstract_id=2845338
..and this one is about how it's done: https://papers.ssrn.com/sol3/papers.cfm?abstract_id=2845871
However, if you don't have data on individual trades, you can use the assumption that prices are driven by the marginal investor and infer utility functions from the pricing kernel: Blackburn and Ukhov share some work on this: https://papers.ssrn.com/sol3/papers.cfm?abstract_id=890592
Hope that helps. Thomas
