Geodesic
Historical share's behavior accounting
Matematičeskoe modelirovanie, Tome 15 (2003) no. 12, pp. 75-80

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The models where stock is a lognormal distributed random process are the routine ones. But these models ignore a possible sensitivities of a share's price to the last quotations. In present paper a mathematical model of such kind “memory” accounting is proposed. The model is in concordance with basis postulates of financial mathematics. A contribution of historical stock's behavior is taking into account as additive component in stochastic differential. The effect of the “memory” presence is characterized by time interval $\tau$ that defines the size of the “memory” in the past. A size of the contribution from moment passed is described by weight function. 
@article{MM_2003_15_12_a4,
     author = {D. N. Zhabin},
     title = {Historical share's behavior accounting},
     journal = {Matemati\v{c}eskoe modelirovanie},
     pages = {75--80},
     publisher = {mathdoc},
     volume = {15},
     number = {12},
     year = {2003},
     language = {ru},
     url = {http://geodesic.mathdoc.fr/item/MM_2003_15_12_a4/}
}
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D. N. Zhabin. Historical share's behavior accounting. Matematičeskoe modelirovanie, Tome 15 (2003) no. 12, pp. 75-80. http://geodesic.mathdoc.fr/item/MM_2003_15_12_a4/