Controlled diffusions with boundary-crossing costs
This paper considers the problem of controlling a nondegenerate diffusion in a bounded domain with a cost associated with the number of boundary- crossings of a subdomain before exiting from the original domain. The existence of optimal Markov controls is established by compactness arguments. The dynamic programming formalism is introduced and a verification theorem for optimal Markov controls is proved.
scientific article; zbMATH DE number 4050695