On a class of semi-elliptic diffusion models. Part I: a constructive analytical approach for global existence, densities, and numerical schemes

Details On a class of semi-elliptic diffusion models. Part I: a constructive analytical approach for global existence, densities, and numerical schemes On a class of semi-elliptic diffusion models. Part I: a constructive analytical approach for global existence, densities, and numerical schemes

2010-02-26

arxiv.org/abs/1002.5031v5

Mathematics

Analysis of PDEs

39 pages, Analysis of v2 is extended to operators which satisfy Hoermander condition on a subspace, some misprints in v3 corre

Scientific paper

Semi-elliptic stochastic differential equations (SDEs) are common models among practitioners. However, value functions and sensitivities of such models are described by degenerate parabolic partial differential equations (PDEs) where the existence of regular global solutions is not trivial, and where densities do not exist in spaces of measurable functions but only in a distributional sense in general. In this paper, we show that for a related class of such equations regular global solutions can be constructed. Moreover, the solution scheme has a probabilistic interpretation where the existence of regular densities on certain subspaces of the state space can be exploited. Prominent examples of models of practical interest belonging to this class include factor reduced LIBOR market models and Cheyette models. A factor reduced SDE originating from a full factor model will likely be within the class where our theorem applies. The result is also of interest for the theory of degenerate parabolic equations. A more detailed analysis of numerical and computational issues, as well as quantitative experiments will be content of the second part.

Affiliated with

Also associated with

No associations

Rating

On a class of semi-elliptic diffusion models. Part I: a constructive analytical approach for global existence, densities, and numerical schemes does not yet have a rating. At this time, there are no reviews or comments for this scientific paper.

If you have personal experience with On a class of semi-elliptic diffusion models. Part I: a constructive analytical approach for global existence, densities, and numerical schemes, we encourage you to share that experience with our LandOfFree.com community. Your opinion is very important and On a class of semi-elliptic diffusion models. Part I: a constructive analytical approach for global existence, densities, and numerical schemes will most certainly appreciate the feedback.

Rate now

Comments { 0 }

Profile ID: LFWR-SCP-O-290126