I am interested in the following optimal stopping problem:
- On each day, a number $a_i$ is drawn from a (possibly fixed) distribution.
- I can either stop now, getting a payoff of $a_i$, or wait for a later draw.
- In principle, this could go on forever. However, future payoffs are discounted at a (possibly constant) rate.
I know this kind of problem has been analysed extensively. Can anyone recommend some references on how one characterises optimal strategies in this context?