Timeline for Variable Drift Ornstein–Uhlenbeck Process

9 events

when toggle format	what		by	license	comment
Jun 12, 2015 at 14:38	vote	accept	ght
Jun 12, 2015 at 14:38	vote	accept	ght
Jun 12, 2015 at 14:38
Jun 12, 2015 at 14:28	comment	added	ght		@Gordon: Unfortunately, I don't have that book. Is there any other open source reference? If not could you please write the expression? Thanks!
Jun 12, 2015 at 14:24	comment	added	Ulysses		@Gordon: indeed, I never used that $p$ is the proper period, can be any value at which the function repeats itself.
Jun 12, 2015 at 14:23	comment	added	Gordon		There is a general solution, in integral form, for $x_t$. See Formula (3.35) in the book "Interest rate models - theory and practice - second edition" by Brigo.
Jun 12, 2015 at 14:19	comment	added	Gordon		If $f\equiv \mu$, then $F=\frac{\mu}{\theta}(e^{\theta p}-1)$. That is, you do not need the limit for $p\rightarrow 0$.
Jun 12, 2015 at 14:16	comment	added	ght		Thanks Ulysses. It makes sense. I also realized that if we consider the process $dx_t=\theta(f(t)+\frac{f'(t)}{\theta} -x_t)dt+\sigma dB_t$ then $m_t=x_0\exp(-\theta t)+f(t)-f(0)\exp(-\theta t)$. Do you know if there a closed form solution to x_t in the general case?
Jun 12, 2015 at 14:09	history	edited	Ulysses	CC BY-SA 3.0	added 215 characters in body
Jun 12, 2015 at 13:24	history	answered	Ulysses	CC BY-SA 3.0