Optimal stopping value function
= Optimal stopping value function
{title2=$V(t,s)$}
For a <Markov process> with reward $f$, the value starting at time $t$ in state $s$ is the supremum of expected rewards over admissible <stopping times>. In finite discrete time it obeys $V(T,s)=f(s)$ and $V(t,s)=\max\{f(s),PV(t+1,\cdot)(s)\}$ for the <transition operator> $P$, wherever expectations are well-defined. Statewise absolute integrability of every remaining-horizon reward makes these values finite.