Hi,

I study a financial market model which is an extension of the famous
multimdimensional Black-Scholes-Model. By using matrices to model the
volatility it is possible to model directly interacting assets.
By this special construction the solution of the stochastic
differential equation describing the evolution of the assets can reach
zero or become negative.
If one assumes that the risky assets remain strictly positive you can
find conditions under which the market model is complete.
I want to consider especially the case what happens if the assets
reachs zero. Therefore I am looking for some papers or preprints
dealing with a financial market studying the case that risky assets
reachs the origin. Maybe there exist some investigations of financial
markets where the risky assets are modelled by making use of poisson
processes or levy processes.

If you have any idea, please send me your hint.

Thank you very much!

Kai wrote:

Hi,

I study a financial market model which is an extension of the famous
multimdimensional Black-Scholes-Model. By using matrices to model the
volatility it is possible to model directly interacting assets.
By this special construction the solution of the stochastic
differential equation describing the evolution of the assets can reach
zero or become negative.
If one assumes that the risky assets remain strictly positive you can
find conditions under which the market model is complete.
I want to consider especially the case what happens if the assets
reachs zero. Therefore I am looking for some papers or preprints
dealing with a financial market studying the case that risky assets
reachs the origin. Maybe there exist some investigations of financial
markets where the risky assets are modelled by making use of poisson
processes or levy processes.

If you have any idea, please send me your hint.

Thank you very much!

I am not in proc models - but by assumption your process stops
even for dim=1 (practically: if the asset does no longer exist
all options break down). May be you ask for some default or
ruin probability? Google should give you a lot on finance +
Poisson or Levy - for example 'Carr', 'Eberlein', 'Schoutens'
'Schoenbucher' among many others.

--
remove the no to mail me

http://www.ingber.com/path01_pathtree.pdf is an algorithm that develops
quite generally nonlinear diffusuon processes. This has been used for
precise options calculations, including models including negative
security prices (important for some interest-rate products).

Lester

In article ,
Kai wrote:
:Hi,
:
:I study a financial market model which is an extension of the famous
:multimdimensional Black-Scholes-Model. By using matrices to model the
:volatility it is possible to model directly interacting assets.
:By this special construction the solution of the stochastic
:differential equation describing the evolution of the assets can reach
:zero or become negative.
:If one assumes that the risky assets remain strictly positive you can
:find conditions under which the market model is complete.
:I want to consider especially the case what happens if the assets
:reachs zero. Therefore I am looking for some papers or preprints
:dealing with a financial market studying the case that risky assets
:reachs the origin. Maybe there exist some investigations of financial
:markets where the risky assets are modelled by making use of poisson
rocesses or levy processes.
:
:If you have any idea, please send me your hint.
:
:Thank you very much!


--
Prof. Lester Ingber
www.ingber.com www.alumni.caltech.edu/~ingber