Constructing mathematical models for the stock market has a long history. One of the models that is used to describe the market growth when changes occur as "normal events" is the Geometric Brownian Motion. Other models extend the GBM by including the possibility of "rare events" that happen randomly according to a Poisson distribution. There are attempts to use the Levy stable distributions without finite second moment, and there are still other models used.

In this talk we will apply the Geometric Brownian Motion to model the growth of equity funds in the case when the sampling interval is sufficiently long (one month or more) so the GBM model is a good approximation. The question is asked: what happens when this random process is disturbed periodically by taking out money from the fund through a cushion of "stable accounts" like fixed investments. One can derive a Markov chain with an infinite state space and study the following questions:

1. What is the chance to get broke when more (or less) money is taken out than average growth rate generates? Is P(eventual zero balance) = 1 ?
2. How does the chance of getting broke depend on the current balance?
3. How long it takes to get broke, if that happens at all?
4. What is the distribution of "time-to-zero-balance" data?
5. Other interesting facts.