homogenize

Analytical formulas for survival in regime switching Orstein-Uhlenbeck processes

Hi there

This package exists for one purpose only: estimation of survival probability for a triply stochastic regime switching process using a fairly advanced technique, asymptotic homogenization. I'm still tinkering with it and there might yet be bugs ... so caveat emptor. The calculation is from the back of my phd thesis 18 years ago so I'm a bit rusty :) The technique is not like a series expansion that is more accurate near t=0, rather it is more accurate for larger t. A little counterintuitive. It needs to be used with care and I recommend running the simulations to get a sense.

If you are truly interested there is a draft shared on Overleaf: https://www.overleaf.com/read/rqkgmnqfsvvm If you discover a bug in the maple code for generating the series expansion or the python code it is translated to I will be forever greatful.

-Peter

Usage

To use the survival probability estimator

from homogenize import RegimeSwitchingModel
params = {'kappa': 2.0, 'thetas': [0.15, 0.02], 'sigmas': [math.sqrt(0.0555), math.sqrt(0.0055)], 'lmbd': 1.7}
model = RegimeSwitchingModel(**params)
model.u(x=0.12,t=7.2) 

To check against simulation

from homogenize import demo
demo()