×
Well done. You've clicked the tower. This would actually achieve something if you had logged in first. Use the key for that. The name takes you home. This is where all the applicables sit. And you can't apply any changes to my site unless you are logged in.

Our policy is best summarized as "we don't care about _you_, we care about _them_", no emails, so no forgetting your password. You have no rights. It's like you don't even exist. If you publish material, I reserve the right to remove it, or use it myself.

Don't impersonate. Don't name someone involuntarily. You can lose everything if you cross the line, and no, I won't cancel your automatic payments first, so you'll have to do it the hard way. See how serious this sounds? That's how serious you're meant to take these.

×
Register


Required. 150 characters or fewer. Letters, digits and @/./+/-/_ only.
  • Your password can’t be too similar to your other personal information.
  • Your password must contain at least 8 characters.
  • Your password can’t be a commonly used password.
  • Your password can’t be entirely numeric.
Enter the same password as before, for verification.
Login

Grow A Dic
Define A Word
Make Space
Set Task
Mark Post
Apply Votestyle
Create Votes
(From: saved spaces)
Exclude Votes
Apply Dic
Exclude Dic

Polynomial interacting particle systems and non-linear SPDEs for market capitalization curves

Click here to flash read.

arXiv:2404.10744v2 Announce Type: replace
Abstract: Motivated by the robustness of the capital distribution curves, we study the behavior of a certain polynomial equity market model as the number of companies goes to infinity. More precisely, we extend volatility-stabilized market models introduced by Fernholz et al. by allowing for a common noise term such that the models remain polynomial. As the number of companies approaches infinity, we show that the limit of the empirical measure of the $N$-company system converges to the unique solution of a degenerate, non-linear SPDE. The obtained limit also has a representation as the conditional probability of the solution to a certain McKean-Vlasov SDE. Together with its conditional, this is again a polynomial process for which we can prove pathwise uniqueness as well as regularity properties for the marginal densities. We also provide conditional propagation of chaos results and numerical implementations of the particle system as well as its limiting equations.

Click here to read this post out
ID: 813401; Unique Viewers: 0
Unique Voters: 0
Total Votes: 0
Votes:
Latest Change: April 19, 2024, 7:32 a.m. Changes:
/u/anonymous
Dictionaries:
Words:
Spaces:
Views: 9
CC:
No creative common's license
Comments: