The shape of the value function under Poisson optimal stopping

In a classical problem for the stopping of diffusion process ( X t ) ? 0 , where goal is to maximise expected discounted value function stopped E x [ e ? ? ? g ] maximisation takes place over all times . Poisson optimal problem, restricted event an independent process. this article we consider whether resulting V ? = sup ? T (where supremum taken taking values in inhomogeneous with rate inherits monotonicity and convexity properties from It turns out that (respectively convexity) depends on quantity + rather than Our main technique stochastic coupling.