# Optimal order placement in limit order markets

I am reading the paper: https://sci-hub.do/10.1080/14697688.2016.1190030 because I want to split the target shares in market order book and limit order book.

I have a question when it comes to page 10 in section: Numerical convergence.

The author used pmf of Poisson distribution and chose $$\lambda$$ = 2200. But, I think it is so large to calculate. I don't know that I misinterpreted the author's meaning or if there's some confusion.

• Why do you think it is too large to calculate? It is a Poisson random variable and the rate parameter, $\mu$, has support on $(0,\infty)$.
• I use the fomular of probability mass function (pmf), we have $e^{-\lambda} = e^{-2200} \to 0$. This is my problem. Jan 19 at 10:01
• This is not how you simulate a Poisson random variable. In general, you can utilize that the waiting times are exponentially distributed, ie. that $Y(i)\sim exp(\mu)$ and then saying that the Poisson has occurances at $t=Y(0),Y(0)+Y(1),Y(0)+Y(1)+Y(2),..$ implying that $Y(i)$ is the time between events $i-1$ and $i$. You can read this, and search on google on how to implement a Poisson random generator, however, majority of programming languages already have a built-in function for this.