## Bernoulli

• Bernoulli
• Volume 19, Number 3 (2013), 931-953.

### On data-based optimal stopping under stationarity and ergodicity

#### Abstract

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.

#### Article information

Source
Bernoulli, Volume 19, Number 3 (2013), 931-953.

Dates
First available in Project Euclid: 26 June 2013

https://projecteuclid.org/euclid.bj/1372251148

Digital Object Identifier
doi:10.3150/12-BEJ439

Mathematical Reviews number (MathSciNet)
MR3079301

Zentralblatt MATH identifier
1273.62192

#### Citation

Kohler, Michael; Walk, Harro. On data-based optimal stopping under stationarity and ergodicity. Bernoulli 19 (2013), no. 3, 931--953. doi:10.3150/12-BEJ439. https://projecteuclid.org/euclid.bj/1372251148

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