Some possible stock price distributions under incompleteness of the market

In this paper, we consider stock price models which are simple generalizations of the binary models. We consider the case when more than two jumps are possible at each trading time. This assumption leads us to incompleteness of the market. Then, on the analogy of the classical case, we study the possible limit laws for the stock price at the terminal date as the number of the trading times goes to infinity and the possible jumps converge to certain limits. We show that normal and Poisson laws and also their certain combinations are possible in this case and give necessary and sufficient conditions for such limit laws.