I'm looking for an approach that's made-up numbers all the way down.

You may want to rephrase that :-)

Once you have that, there's an exact answer to the optimal risk/reward tradeoff

No, I don't think so. For example, let's say your utility = log(wealth). That's a monotonous transformation, so if you want to maximize utility you just maximize your wealth. That doesn't answer the question of what is the appropriate risk/reward trade-off because you haven't even started talking about risk yet. And if you just want to maximize expected wealth you are open to being Pascal-mugged.

Maximizing expected log(wealth) is very different than maximizing expected wealth. A log utility function us much more risk averse.

The Wikipedia article on VNM Utility Theory explains the relationship between the utility function and risk aversion (in the Consequences section).

Open thread, Apr. 18 - Apr. 24, 2016

by MrMind 1 min read18th Apr 2016176 comments

2


If it's worth saying, but not worth its own post (even in Discussion), then it goes here.


Notes for future OT posters:

1. Please add the 'open_thread' tag.

2. Check if there is an active Open Thread before posting a new one. (Immediately before; refresh the list-of-threads page before posting.)

3. Open Threads should be posted in Discussion, and not Main.

4. Open Threads should start on Monday, and end on Sunday.