Suppose I have to numerically simulate a process $\{y_t\}$ such that $y_t\geq0$ $\forall t\in\mathbb{N}$, with $t$ denoting time-step.

Let's suppose I use MonteCarlo with $\mathscr{N}$ simulation trajectories. Could it occur that sometimes, when running simulation, some of these $\mathscr{N}$ trajectories slightly goes beyond $0$ hence violating the condition of non-negativity of the process?
I mean: should I take this fact as an alert around the incorrectness of my simulation code or is it allowed that numerical simulation can (just "sometimes") give you some trajectories (out of the total $\mathscr{N}$) that slightly deviate from the non-negativity condition?

  • 1
    $\begingroup$ If an individual trajectory has to satisfy some positivity constraint and this condition is sometimes violated then there is a bug in the code. $\endgroup$ – Maxim Umansky Jul 26 at 15:36

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