Compound Poisson process

Dear Zornitsa,

1) Is it right to simulate exponentially distributed waiting times between
the jumps and then just "jump" with a Beta / Pareto distributed magnitude?
  

Depending on what parts of the process are needed (e.g. final values 
only, discrete approximation of process path,...) different techniques 
(which are mentioned in the monograph by Cont/Tankov) may be favourable:

- final values only: sample the number of jumps from 
Poisson(lambda[i]*T) distribution (when T denotes final time) for Beta 
[1] and Pareto [2] jumps and sum up simulated jump magnitudes 
accordingly (should be especially efficient when implemented in R 
without using C calls). [If jump times are needed: they are distributed 
uniformly on (0,T).]

- discrete approximation: Beta and Pareto distributed jumps may be 
concentrated in one CP process:
  * draw exponential waiting times (rate = lambda[1]+lambda[2])
  * for each jump: with probability lambda[1]/(lambda[1]+lambda[2]) draw 
Beta jump; draw Pareto jump else.

Kind regards,

  Martin

Dr. Martin Becker
Saarland University
Statistics and Econometrics