CALCULATION OF ASIAN OPTIONS FOR THE BLACK-SCHOLES MODEL

The paper deals with one of fundamental problems of financial mathematics, namely, allocation of resources between financial assets to ensure sufficient payments. When constructing mathematical models of the dynamics of financial indicators, various classes of random processes with discrete and continuous time are used. Therefore, the theory of martingales is a natural and useful mathematical tool in financial mathematics and engineering. In this paper, the Black-Scholes model is considered in continuous time with two financial assets {B-t = 1, dS(t) = sigma S(t)dW(t),S-0 > 0. The representation Theorem 1 of square integrable martingales is studied to calculate coefficients of the martingale representation. These coefficients allow further redistribution of the securities portfolio to obtain the greatest profit.