Timeline for On a stochastic control problem

Current License: CC BY-SA 4.0

12 events

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Mar 7, 2023 at 10:51	history	edited	Fawen90	CC BY-SA 4.0	deleted 877 characters in body; edited title
Feb 17, 2023 at 10:45	history	edited	Fawen90	CC BY-SA 4.0	deleted 1 character in body
Feb 17, 2023 at 9:28	comment	added	Fawen90		@ThomasKojar Thanks for pointing out the typo. It's corrected
Feb 17, 2023 at 9:28	history	edited	Fawen90	CC BY-SA 4.0	edited body
Feb 16, 2023 at 19:41	comment	added	Thomas Kojar		For Q2, it seems unlikely that there is a deterministic such $N$ because the stopping time $\tau^{p,t,x}$ shows up in the integral it varies randomly based on $n$. It would mean that the maximizer $p_{*}$ is almost surely within a deterministic interval $[0,M]$ but that is never case for random objects because it suffices to take some realization $\omega$ where all the $p$ are large.
Feb 16, 2023 at 19:14	comment	added	Thomas Kojar		For Q1, How about we replace the supremum over $p\in \mathcal{U}_{n}$ by over $p\in \mathcal{U}$ by writing $1_{[1/n,n]}p$ inside the expected value? Then it is more of a question of applying Dominated convergence theorem in the expected value and integral.
Feb 16, 2023 at 19:06	comment	added	Thomas Kojar		there are some notation issues to fix first, eg. in the integral you have $\log p_{s}$ but I think you meant $\log p_{u}$. Also, later you again use the same variable $u$ for both integrating and to denote constant control.
Feb 16, 2023 at 12:58	history	edited	Fawen90	CC BY-SA 4.0	edited body
Feb 16, 2023 at 12:48	history	edited	Fawen90	CC BY-SA 4.0	deleted 1 character in body
Feb 16, 2023 at 9:53	history	edited	Fawen90	CC BY-SA 4.0	added 776 characters in body
Feb 16, 2023 at 9:24	history	edited	Fawen90	CC BY-SA 4.0	edited body
Feb 16, 2023 at 9:18	history	asked	Fawen90	CC BY-SA 4.0