Geodesic
On the rational pricing of the “Russian Option” for the symmetrical binomial model of a $(B,S)$-market
Teoriâ veroâtnostej i ee primeneniâ, Tome 39 (1994) no. 1, pp. 191-200 Cet article a éte moissonné depuis la source Math-Net.Ru

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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 $f=(f_n)_{n\ge 0}$ given by $$ f_n(\omega)=\beta^n\max_{k\le n}S_k(\omega), $$ where $\beta$ is some discounting factor, $0<\beta<1$. This option was introduced earlier by L. Sheep and A. N. Shiryaev [3], in the framework of the diffusion model of Black and Sholes.
Mots-clés : the binomial Cox
Keywords: Rubinstein, and Ross model, American option, “Russian option”, symmetric geometrical random walk, optimal stopping rules. 
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     author = {D. O. Kramkov and A. N. Shiryaev},
     title = {On the rational pricing of the {{\textquotedblleft}Russian} {Option{\textquotedblright}} for the symmetrical binomial model of a $(B,S)$-market},
     journal = {Teori\^a vero\^atnostej i ee primeneni\^a},
     pages = {191--200},
     year = {1994},
     volume = {39},
     number = {1},
     language = {ru},
     url = {http://geodesic.mathdoc.fr/item/TVP_1994_39_1_a5/}
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D. O. Kramkov; A. N. Shiryaev. On the rational pricing of the “Russian Option” for the symmetrical binomial model of a $(B,S)$-market. Teoriâ veroâtnostej i ee primeneniâ, Tome 39 (1994) no. 1, pp. 191-200. http://geodesic.mathdoc.fr/item/TVP_1994_39_1_a5/