Stock Prices as Janardan Galton Watson Process

Janardan (1980) introduces a class of offspring distributions that sandwich between Bernoulli and Poisson. This paper extends the Janardan Galton Watson (JGW) branching process as a model of stock prices. In this article, the return value over time t depends on the initial close price, which shows the number of offspring, has a role in the expectation of return and probability of extinction after the passage at time t. Suppose the number of offspring in t th generation is zero, (i.e., called extinction of model at time t) is equivalent with negative return values over time [0, t]. We also introduce the Algorithm that detecting the trend of stock markets.