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 St = S0 exp {( − (2/ 2))t - Wt} and Bt = B0 exp{rt}, t Ўф[0,T], where  > 0, r > 0, S0 > 0, B0 > 0. Current capital value of investor Xt = tBt - tSt , where t = (t , t ) is an investment portfolio. Dividends are paid in accordance with the process Dt at the rate dDt = tStdt ,  > 0. The problem is considered: to find the option price in accordance with the payoff function 0 T ( ) (max t ) t T fS S KЎВ ЎВ = −, where K > 0 is the striking price, as well as the hedging strategy - (-, -) t = t t and capital Xt , which ensures the fulfillment of the payment liability XT- = fT (S).