This note studies a Poisson arrival selection problem for the full-information case with an unknown intensity λ which has a Gamma prior density G(r, 1/a), where a>0 and r is a natural number. For the no-information case with the same setting, the problem is monotone and the one-step look-ahead rule is an optimal stopping rule; in contrast, this note proves that the full-information case is not a monotone stopping problem.
We consider a gradual-impulse control problem of continuous-time Markov decision processes, where the system performance is measured by the expectation of the exponential utility of the total cost. We show, under natural conditions on the system primitives, the existence of a deterministic stationary optimal policy out of a more general class of policies that allow multiple simultaneous impulses, randomized selection of impulses with random effects, and accumulation of jumps. After characterizing the value function using the optimality equation, we reduce the gradual-impulse control problem to an equivalent simple discrete-time Markov decision process, whose action space is the union of the sets of gradual and impulsive actions.
This note studies a Poisson arrival selection problem for the full-information case with an unknown intensity λ which has a Gamma prior density G(r, 1/a), where a>0 and r is a natural number. For the no-information case with the same setting, the problem is monotone and the one-step look-ahead rule is an optimal stopping rule; in contrast, this note proves that the full-information case is not a monotone stopping problem.
Suppose that an unknown number of objects arrive sequentially according to a Poisson process with random intensity λ on some fixed time interval [0, T ]. We assume a gamma prior density G λ (r, 1/a) for λ. Furthermore, we suppose that all arriving objects can be ranked uniquely among all preceding arrivals. Exactly one object can be selected. Our aim is to find a stopping time (selection time) which maximizes the time during which the selected object will stay relatively best. Our main result is the following. It is optimal to select the ith object that is relatively best and arrives at some time s (r) i onwards. The value of s (r) i can be obtained for each r and i as the unique root of a deterministic equation.
scite is a Brooklyn-based organization that helps researchers better discover and understand research articles through Smart Citations–citations that display the context of the citation and describe whether the article provides supporting or contrasting evidence. scite is used by students and researchers from around the world and is funded in part by the National Science Foundation and the National Institute on Drug Abuse of the National Institutes of Health.