Call option on the basis of maximum value of risk asset price with fixed price of execution.
Risk and riskfree assets, circulating in a financial market, have current prices <i>St </i>= <i>S</i>0 exp {( − (2/ 2))<i>t </i>- <i>Wt</i>}<i> </i>and <i>Bt </i>= <i>B</i>0 exp{<i>rt</i>}, <i>t </i>Ўф[0,<i>T</i>], where  > 0, <i>r </i>> 0, <i>S</i>0 > 0, <i>B</i>0 > 0. Current capital value of investor <i>Xt </i>= <i>tBt </i>- <i>tSt </i>, where <i>t </i>= (<i>t </i>, <i>t </i>) is an investment portfolio. Dividends are paid in accordance with the process <i>Dt </i>at the rate <i>dDt </i>= <i>tStdt </i>,  > 0. The problem is considered: to find the option price in accordance with the payoff function 0 <i>T </i>( ) (max <i>t </i>) <i>t T fS S K</i>ЎВ ЎВ = −, where <i>K </i>> 0 is the striking price, as well as the hedging strategy - (-, -) <i>t </i>= <i>t t </i>and capital <i>Xt </i>, which ensures the fulfillment of the payment liability <i>XT</i>- = <i>fT </i>(<i>S</i>).