On the stock price model defined by the fractional Brownian semilinear stochastic differential equation: measure transformation and equilibrium of stock market Yuriy Krvavych 1 Assistant Professor of Probability and Statistics Department, Mechanics and Mathematics Faculty, Taras Shevhenko National University of Kyiv, 64 Volodymyrska str., Kyiv 01033, UKRAINE tel./fax: 380-44-266-23-37, e-mail: krvavych@yahoo.com Head Actuary of Actuarial Department, ”Oranta” Insurance Company, 34/1 Hrushevsky str., Kyiv 01021, UKRAINE tel./fax: 380-44-253-06-59, e-mail: krvavy@oranta.com.ua Abstract The existence and uniqueness conditions for solution of semilinear stochastic differential equations containing a differential with respect to fractional Brownian motion are considered in this paper. Also, for such fractional Brownian semilinear stochastic differential equations the conditions of measure transformation are estab- lished. The equilibrium conditions of stock market that described by the fractional Brownian semilinear stochastic differential equation are found. MSC: Primary 60H05, 60G15, 60G17, 60G44, 60H10 Keywords: fractional Brownian motion, differentiability of stochastic integrals, semilinear stochastic differential equations, measure transformation, equilibrium of financial market. 1 All results of the present paper has been included to author’s Ph.D. thesis on financial mathematics.