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pbillet
Posts:
33
From:
paris
Registered:
9/23/09


Stochastic differential equation, inversion & smib
Posted:
Aug 27, 2011 1:38 AM


The purpose is to simulate the behaviour of a SDE of type dX_{t}=f(X_{t},t)dt+g(X_{t},t)dB_{t} using the method of inversion, the final aim is to compute E(X_{t}) and Var(X_{t}) .
To generate a list of random numbers following a law L :  we build a list of random numbers following the uniform law on [0,1]  then by the method of inversion, we obtain a list of random numbers following the law L.
It is clear that the temporal cost of this method is important. Then to decrease the computation time of the simulations, we do not regenerate a list of random numbers, but for every simulation, we mix randomly the elements of the list. And for the simulation, we simply use the method of EulerMaruyama.
The tests were made on the following cases:  OrnsteinUhlenbeck process,  Vasicek process,  CoxIngersollRoss process.A classic version of simulation (using the uniform law, the BoxMuller transformation, and the method of EulerMaruyama) is used as base of comparison.
On these examples, it seems that we still have reasonable computation time if the parameters are correctly adjusted.
Results can be seen here : http://smib.sourceforge.net/#tocSubsubsection5.7.8 You can download smib here : http://sourceforge.net/projects/smib/ N.B. : you must compile it on you own.



