A note on randomized Shepp’s urn scheme

Shepp’s urn model is a useful tool for analyzing the stopping-rule problems in economics and finance. In [R.W. Chen, A. Zame, C.T. Lin, H. Wu, A random version of Shepp’s urn scheme, SIAM J. Discrete Math. 19 (1) (2005) 149–164], Chen et al. considered a random version of Shepp’s urn scheme and showed that a simple drawing policy (called “the kk in the hole policy”) can asymptotically maximize the expected value of the game. By extending the work done by Chen et al., this note considers a more general urn scheme that is better suited to real-life price models in which the short-term value might not fluctuate. Further, “the kk in the hole policy” is shown to be asymptotically optimal for this new urn scheme.