Recent content by steveO

Thanks, Daniel! Did I miss something in your paper? If possible, could you point out where in the paper the explanation (formal or informal) for X_t might going negative with Euler and/or Milstein schemes is?

Thanks, Daniel! There is no particular usage with the results yet. It is just for learning purpose.

Thanks koupparis! I did googled quite a while but not find anything, unless I missed something?

Thanks Daniel! Just quick looked through the paper. It seems that it doesn't show the probability of CIR going negative under either Euler or Miltein schemes, as it is a paper that proposed ADE method. Would it be possible that some books/tutorials (the more, the better) have some kind of...

Thanks Koupparis! Yes, both actual proof and the condition for X_t staying positive in both Euler and Milstein schemes are what I am looking for, because when all the terms sum up, it is difficult to say why the probability of X_t going negative is bigger than zero, while under some condition...

Thanks Daniel and ThinkDifferent! Nice to know about the other better ways to go! I am still wondering why, in Euler scheme for SDE, the time step must be less than some value to ensure the probability of going negative is zero? Is there also some similar requirement for the Milstein scheme...

Let (X = (X_t: t \in [0,T])) be a stochastic process satisfying a CIR model. (dX_t = \beta (X_t - \gamma) dt + \sigma\sqrt{X_t} dB_t,) where (B_t) is a standard Brownian motion, (\beta) is a negative constant, (\gamma, \sigma) are positive constants. In order for the SDE to make sense, assume...