The problem of optimal stopping with finite horizon in discrete time
is considered in view of maximizing the expected gain. The algorithm
presented in this talk is completely nonparametric in the sense that it
uses observed data from the past of the process up to time -n+1 (n being
a natural number), not relying on any specific model assumption. Kernel
regression estimation of conditional expectations and prediction theory
of individual sequences are used as tools.
The main result is that the algorithm is universally consistent: the
achieved expected gain converges to the optimal value for n tending to
infinity, whenever the underlying process is stationary and ergodic.
An application to exercising American options is given.
- Nomura Seminar