We present in the binomial model of Cox, Rubinstein and Ross the closed form solution for the “Russian option”, i.e., the American type option with the reward sequence f = (fₙ )n 0 given by \[ f_n (ω ) = β ^n {max }k n S_k (ω ), \] where β is some discounting factor, 0 < β < 1. This option was introduced earlier by L. Sheep and A. N. Shiryaev [3], in the framework of the diffusion model of Black and Sholes.
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Kramkov et al. (1995) studied this question.