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August 2013 On data-based optimal stopping under stationarity and ergodicity
Michael Kohler, Harro Walk
Bernoulli 19(3): 931-953 (August 2013). DOI: 10.3150/12-BEJ439


The problem of optimal stopping with finite horizon in discrete time is considered in view of maximizing the expected gain. The algorithm proposed in this paper is completely nonparametric in the sense that it uses observed data from the past of the process up to time $-n+1$, $n\in\mathbb{N}$, not relying on any specific model assumption. Kernel regression estimation of conditional expectations and prediction theory of individual sequences are used as tools. It is shown that the algorithm is universally consistent: the achieved expected gain converges to the optimal value for $n\to\infty$ whenever the underlying process is stationary and ergodic. An application to exercising American options is given, and the algorithm is illustrated by simulated data.


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Michael Kohler. Harro Walk. "On data-based optimal stopping under stationarity and ergodicity." Bernoulli 19 (3) 931 - 953, August 2013.


Published: August 2013
First available in Project Euclid: 26 June 2013

zbMATH: 1273.62192
MathSciNet: MR3079301
Digital Object Identifier: 10.3150/12-BEJ439

Rights: Copyright © 2013 Bernoulli Society for Mathematical Statistics and Probability


Vol.19 • No. 3 • August 2013
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