Timeline for Another large noise limit
Current License: CC BY-SA 4.0
24 events
| when toggle format | what | by | license | comment | |
|---|---|---|---|---|---|
| Apr 22, 2022 at 2:04 | comment | added | Nate River | Thanks a lot! They look very informative. Now time to read.. | |
| Apr 21, 2022 at 21:15 | comment | added | Iosif Pinelis | I have now added such heuristics. | |
| Apr 21, 2022 at 17:20 | comment | added | Iosif Pinelis | I will try to add such heuristics later, on why one conjecture holds and the other fails. I think this can also be discerned by analyzing the sources and contributions of the various terms in the expressions for $\text{num}$ and $\text{den}$ in my answer, even though I have not done such work. | |
| Apr 21, 2022 at 16:05 | comment | added | Nate River | It would be quite enlightening to know intuitively why the current conjecture fails, while the simpler one in the linked post holds true. | |
| S Apr 21, 2022 at 16:03 | history | bounty ended | Nate River | ||
| S Apr 21, 2022 at 16:03 | history | notice removed | Nate River | ||
| Apr 21, 2022 at 15:58 | comment | added | Nate River | As for motivation, this arose in trying to derive asymptotic bounds on the price of short maturity Asian options, modelled as geometric Brownian motion. | |
| Apr 21, 2022 at 15:58 | comment | added | Nate River | Thank you for your detailed answer. I arrived at the conjecture by guessing that conditional on $\max_{0 \leq t \leq 1} W_t \geq M$, then formally $\frac{1}{M} dW_t$ behaves as $dt$ as $M \to \infty$. (The condition on the corresponding max for $X$ translates directly to a condition of this form on $W$.) Thus the SDE $dX_t = \sigma X_t dW_t$ formally becomes $dX_t = M \sigma X_t dt$, which admits solution $X = e^{M \sigma t}$. The normalisation $C(\varepsilon)$ is then simply $M \sigma$. | |
| Apr 21, 2022 at 15:56 | vote | accept | Nate River | ||
| Apr 21, 2022 at 4:37 | history | edited | Iosif Pinelis |
edited tags
|
|
| Apr 21, 2022 at 4:08 | answer | added | Iosif Pinelis | timeline score: 1 | |
| Apr 20, 2022 at 20:36 | comment | added | Iosif Pinelis | Can you disclose how you arrived at this conjecture, in particular, to $e^t$? Are you sure your expression for $C(\varepsilon)$ is correct? | |
| S Apr 15, 2022 at 10:31 | history | bounty started | Nate River | ||
| S Apr 15, 2022 at 10:31 | history | notice added | Nate River | Draw attention | |
| Apr 15, 2022 at 10:28 | history | edited | Nate River | CC BY-SA 4.0 |
added 29 characters in body
|
| Apr 10, 2022 at 13:35 | history | edited | Nate River | CC BY-SA 4.0 |
added 24 characters in body
|
| Apr 10, 2022 at 13:20 | history | edited | Nate River | CC BY-SA 4.0 |
added 3 characters in body
|
| Apr 10, 2022 at 13:14 | history | edited | Nate River | CC BY-SA 4.0 |
added 86 characters in body
|
| Apr 10, 2022 at 13:12 | history | undeleted | Nate River | ||
| Apr 10, 2022 at 13:01 | history | deleted | Nate River | via Vote | |
| Apr 6, 2022 at 17:02 | history | edited | Nate River | CC BY-SA 4.0 |
added 262 characters in body
|
| Apr 6, 2022 at 17:00 | history | undeleted | Nate River | ||
| Apr 6, 2022 at 16:57 | history | deleted | Nate River | via Vote | |
| Apr 6, 2022 at 16:47 | history | asked | Nate River | CC BY-SA 4.0 |