УПРАВЛЕНИЕ ДИНАМИЧЕСКИМИ СИСТЕМАМИ ПРИ ОГРАНИЧЕНИЯХ НА ВХОДНЫЕ И ВЫХОДНЫЕ СИГНАЛЫ

Abstract

Risk and riskfree assets, circulating in a financial market, have current prices St = S0 exp {(ƒ − (ƒ2/ 2))t ƒWt} and Bt = B0 exp{rt}, t Ўф[0,T], where ƒ > 0, r > 0, S0 > 0, B0 > 0. Current capital value of investor Xt = ƒtBt ƒtSt , where ƒt = (ƒt , ƒt ) is an investment portfolio. Dividends are paid in accordance with the process Dt at the rate dDt = ƒƒtStdt , ƒ > 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 ƒ(ƒ-, ƒ-) t = t t and capital Xt , which ensures the fulfillment of the payment liability XT= fT (S).