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On the convergence from discrete to continuous time in an optimal stopping problem. (English) Zbl 1138.93066

The optimal stopping problem with two classes of stopping times is considered for a one-dimensional diffusion process with time-independent and Lipschitz continuous coefficients. The first class consists of all stopping times with values in \([0,\infty]\), and the second one of all stopping times with values in the time grid \(\{0,h,2h,\dots,\infty\}\), \(h> 0\). The exact convergence rates, as \(h\to 0\), are presented both for the value functions and the boundaries of stopping regions.

MSC:

93E20 Optimal stochastic control
93E35 Stochastic learning and adaptive control
60J55 Local time and additive functionals
90C59 Approximation methods and heuristics in mathematical programming
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