Geodesic
Some properties of Kagi and Renko moments for Brownian motion
Vestnik Moskovskogo universiteta. Matematika, mehanika, no. 2 (2012), pp. 29-34

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The probabilistic characteristics of Kagi and Renko techniques are studied in the paper. Within the framework of the Bachelier model, a formula for expected gain of a trader following the Kagi strategy is derived. In addition, some properties of the “range” and ‘downfall’' of the Brownian motion are obtained. 
@article{VMUMM_2012_2_a6,
     author = {M. A. Spiryaev},
     title = {Some properties of {Kagi} and {Renko} moments for {Brownian} motion},
     journal = {Vestnik Moskovskogo universiteta. Matematika, mehanika},
     pages = {29--34},
     publisher = {mathdoc},
     number = {2},
     year = {2012},
     language = {ru},
     url = {http://geodesic.mathdoc.fr/item/VMUMM_2012_2_a6/}
}
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M. A. Spiryaev. Some properties of Kagi and Renko moments for Brownian motion. Vestnik Moskovskogo universiteta. Matematika, mehanika, no. 2 (2012), pp. 29-34. http://geodesic.mathdoc.fr/item/VMUMM_2012_2_a6/