The Explicit Chaotic Representation of the powers of increments of Levy Processes

Details The Explicit Chaotic Representation of the powers of increments of Levy Processes The Explicit Chaotic Representation of the powers of increments of Levy Processes

2007-06-12

arxiv.org/abs/0706.1698v2

Mathematics

Probability

41 pages

Scientific paper

An explicit formula for the chaotic representation of the powers of increments, (X_{t+t_0}-X_{t_0})^n, of a Levy process is presented. There are two different chaos expansions of a square integrable functional of a Levy process: one with respect to the compensated Poisson random measure and the other with respect to the orthogonal compensated powers of the jumps of the Levy process. Computationally explicit formulae for both of these chaos expansions of (X_{t+t_0}-X_{t_0})^n are given in this paper. Simulation results verify that the representation is satisfactory. The CRP of a number of financial derivatives can be found by expressing them in terms of (X_{t+t_0}-X_{t_0})^n using Taylor's expansion.

Affiliated with

Also associated with

No associations

Rating

The Explicit Chaotic Representation of the powers of increments of Levy Processes 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 The Explicit Chaotic Representation of the powers of increments of Levy Processes, we encourage you to share that experience with our LandOfFree.com community. Your opinion is very important and The Explicit Chaotic Representation of the powers of increments of Levy Processes will most certainly appreciate the feedback.

Rate now

Comments { 0 }

Profile ID: LFWR-SCP-O-359669