High order discretization schemes of SDEs by using free Lia algebra valued random variables are introduced by Kusuoka, Lyons-Victoir, Ninomiya-Victoir and Ninomiya-Ninomiya etc . These schemes are called KLNV method. These scheme involves solving flow of vector fields usually by numerical method . The authors found the special Lie algebraic structure on the vector fields in the measure financial diffusion models. Using this structure, the flow associated with vector fields can be solved analytically , and enable the high speed computation .
High order discretization schemes of SDEs by using free Lie algebra valued random variables are introduced by Kusuoka, Lyons-Victoir, Ninomiya-Victoir and Ninomiya-Ninomiya . These schemes are called KLNV methods. They involve solving the flows of vector fields associated with SDEs and it is usually done by numerical methods . The authors found a special Lie algebraic structure on the vector fields in the major financial diffusion models. Using this structure, we can solve the flows associated with vector fields analytically and efficiently. Numerical examples show that our method saves the computation time drastically .
R
Lia
Lie
D
etc
R
method. These scheme involves solving flow
methods. They involve solving the flows
R
usually by numerical method
associated with SDEs and it is usually done by numerical methods
R
the
a
R
measure
major
R
the flow
we can solve the flows
R
can be solved analytically , and enable the high speed computation
analytically and efficiently. Numerical examples show that our method saves the computation time drastically