A note on optimal stopping of regular diffusions under random discounting. Theory of Probability and its Applications

Summary. Let X be a one-dimensional regular diffusion, A a positive continuous additive functional of X, and h a measurable real-valued function. A method is proposed to determine a stopping rule T ∗ that maximizes E{e−ATh(XT)1{T<∞}} over all stopping times T of X. Several examples, some related to Mathematical Finance, are discussed. AMS 1991 subject classifications. 60G40, 60J60