Timeline for Enlargement of filtration
Current License: CC BY-SA 4.0
6 events
| when toggle format | what | by | license | comment | |
|---|---|---|---|---|---|
| Jun 30, 2022 at 0:10 | vote | accept | Nate River | ||
| Jun 29, 2022 at 19:49 | comment | added | Christophe Leuridan | Ah yes, you assume that $\mathcal{F}$ is the natural filtration of $M$. Anyway, the answer is negative, see the answer below. | |
| Jun 29, 2022 at 19:47 | answer | added | Christophe Leuridan | timeline score: 4 | |
| Jun 29, 2022 at 15:34 | comment | added | Nate River | Thanks for your comment - though counterexamples like the null martingale are ruled out by the condition that $\mathcal F_t \setminus \mathcal F_s$ be nontrivial. | |
| Jun 29, 2022 at 14:22 | comment | added | Christophe Leuridan | I you wish the condition to be necessary (I think it it not, but for the moment, I have no counterexample), you should at least assume that ALL $\mathcal{F}$-martingales are still $\mathcal{H}$-martingales. This property is called immersion of filtrations. Otherwise, the null martingale provides trivial counterexamples. | |
| Jun 29, 2022 at 13:23 | history | asked | Nate River | CC BY-SA 4.0 |