People are not rational expected utility maximisers.  When we have to make decisions, all sorts of cognitive biases and distortions come into play.  Seminal work in this area was done by Kahneman and Tversky.  They produced a model of human decision making known as prospect theory, work that Kahneman later won a Noble prize ...

... I looked at these investors and thought, “Hey, they’re just like reinforcement learning agents. No big deal. If I want to know what investors with probability weighting and a curved value function do, I can just brute force compute their optimal policy by writing down their Bellman equation and using dynamic programming. Easy!” It was a mystery to me why, seemingly, nobody else was doing that. So off I went to build software to do just this, starting with a simple Merton model…

... When we fired up my simulator and gave this distribution to an investor that had probability weighting: the investor took one look at that scary negative tail and didn’t want to invest in the stock. This is exactly what the model should predict.  In short, we took realistic stock returns, and presented this to an investor with a realistic decision making process complete with a bunch of parameters that have been empirically estimated by others in previous work, and what we got out the other end was realistic investor behaviour!

Read the whole article here at Vetta Project.