$X=M+A$ bounded semimartingale, then $M$ and $A$ are bounded? Counterexample?

49 Views Asked by At
  1. Let be $X=M+A$ a semimartingale with $M$ being a local martingale and $A$ an adapted process a finite variation. If $M$ and $A$ are bounded, then of course $X$ is bounded as well. Is the converse true? Do you have a counterexample?
  2. If not, provided $X$ and $[X]$ are bounded, can we conclude $M$ and $A$ to be bounded? Or is there again a counterexample?