Convergence for step-line processes under summation of random indicators and models of market pricing (Q1781635)

The paper deals with random step-line and broken-line processes defined by sums of independent identically distributed random variables multiplied by values of indicators defined on another probability space and independent in each string. The authors consider two different types of replacements; summands are replaced randomly either by zeros or by nonzero random variables. The functional limit theorems in the case of the same probability space for indicators and random variables are obtained. Some applications in financial mathematics are considered. Namely, for three models of financial market, with constant number of agents, with increasing number of agents and decreasing number of agents, the authors obtain analogs of the Black-Scholes formula.