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A note on optimal stopping of regular diffusions under random discounting

M. Beibel, H. R. Lerche

Institut für Mathematische Stochastik, Universität Freiburg, Germany

Abstract: 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 $\mathbf{E}\{e^{-A_T} h(X_T) 1_{\{T < \infty\}}\}$ over all stopping times $T$ of $X$. Several examples are discussed.

Keywords: diffusions, generalized parking problems, optimal stopping, random regret.

Received: 04.02.1999

Language: English

DOI: 10.4213/tvp497

 English version: Theory of Probability and its Applications, 2001, 45:4, 547–557

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