Optimal Stopping of the Maximum Process: The Maximality Principle
نویسنده
چکیده
where S = (St)t 0 is the maximum process associated with the one-dimensional time-homogeneous diffusion X = (Xt)t 0 , the function x 7! c(x) is positive and continuous, and the supremum is taken over all stopping times of X for which the integral has finite expectation. It is proved, under no extra conditions, that this problem has a solution, i.e. the payoff is finite and there is an optimal stopping time, if and only if the following maximality principle holds: the first-order nonlinear differential equation
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