Question

$\exists c \in\mathbb{R}_+^*,\forall p,r\in \mathbb{R}_+,E[|X_{p+r}-X_r||\mathcal{F}_r] \leq c$ implies the optional stopping theorem

score 114 · Answer 1 · 2026-04-03 06:55:03

114

Views

$\exists c \in\mathbb{R}_+^*,\forall p,r\in \mathbb{R}_+,E[|X_{p+r}-X_r||\mathcal{F}_r] \leq c$ implies the optional stopping theorem

Published on 03 Apr 2026 - 6:55

score 303 · Answer 2 · 2021-08-06 11:01:23

303

Views

Find a probability measure $\mathbb{Q}$, such that $\tilde{S} = e^{-rt}S_t$ is an $\mathbb{F}$-martingale

Published on 06 Aug 2021 - 11:01

score 109 · Answer 3 · 2021-08-09 00:09:39

109

Views

If $\lim_k \mathcal{F}_k=\mathcal{W}$ then $\lim_{k \to \infty} E[X\mid\mathcal{F}_k]=E[X\mid\mathcal{W}]$ a.s?

Published on 09 Aug 2021 - 0:09

score 95 · Answer 4 · 2026-03-31 17:49:33

95

Views

Does the converse of Girsanov theorem hold in this case?

Published on 31 Mar 2026 - 17:49

score 157 · Answer 5 · 2026-04-12 15:44:35

157

Views

Transformation of sub-martingale and super-martingale

Published on 12 Apr 2026 - 15:44

score 101 · Answer 6 · 2026-04-12 10:04:05

101

Views

Exponential martingales of Levy process conditioned on $\sigma$-algebra generated by stopping time

Published on 12 Apr 2026 - 10:04

score 209 · Answer 7 · 2021-08-12 12:27:54

209

Views

Show that $S_n$ is a martingale

Published on 12 Aug 2021 - 12:27

score 87 · Answer 8 · 2026-04-11 20:05:01

87

Views

Probability the walk terminates

Published on 11 Apr 2026 - 20:05

score 278 · Answer 9 · 2026-04-08 15:49:46

278

Views

How do I determine the expected duration of the walk until absorption at either boundary?

Published on 08 Apr 2026 - 15:49

score 545 · Answer 10 · 2026-04-11 20:47:05

545

Views

General version of the fundamental theorem of asset pricing in continuous time

Published on 11 Apr 2026 - 20:47

score 199 · Answer 11 · 2026-04-12 18:42:44

199

Views

If the positive part of submartingale is uniformly integrable, it is closable

Published on 12 Apr 2026 - 18:42

score 319 · Answer 12 · 2026-04-07 06:16:20

319

Views

Proving the discounted stock price is martingale

Published on 07 Apr 2026 - 6:16

score 347 · Answer 13 · 2021-08-19 12:53:10

347

Views

Show that $\mathbb{E}(\lim_{n\to\infty} X_n|\mathcal{F}_n)\ge X_n$ for $(X_n)_{n\ge 0}$ a UI submartingale

Published on 19 Aug 2021 - 12:53

score 302 · Answer 14 · 2026-04-10 13:57:07

302

Views

Understanding the martingale property

Published on 10 Apr 2026 - 13:57

score 291 · Answer 15 · 2026-04-12 19:53:58

291

Views

Showing the Itô logarithm is the inverse of the Doléans-Dade exponential

Published on 12 Apr 2026 - 19:53

List Question

$\exists c \in\mathbb{R}_+^*,\forall p,r\in \mathbb{R}_+,E[|X_{p+r}-X_r||\mathcal{F}_r] \leq c$ implies the optional stopping theorem

Find a probability measure $\mathbb{Q}$, such that $\tilde{S} = e^{-rt}S_t$ is an $\mathbb{F}$-martingale

If $\lim_k \mathcal{F}_k=\mathcal{W}$ then $\lim_{k \to \infty} E[X\mid\mathcal{F}_k]=E[X\mid\mathcal{W}]$ a.s?

Does the converse of Girsanov theorem hold in this case?

Transformation of sub-martingale and super-martingale

Exponential martingales of Levy process conditioned on $\sigma$-algebra generated by stopping time

Show that $S_n$ is a martingale

Probability the walk terminates

How do I determine the expected duration of the walk until absorption at either boundary?

General version of the fundamental theorem of asset pricing in continuous time

If the positive part of submartingale is uniformly integrable, it is closable

Proving the discounted stock price is martingale

Show that $\mathbb{E}(\lim_{n\to\infty} X_n|\mathcal{F}_n)\ge X_n$ for $(X_n)_{n\ge 0}$ a UI submartingale

Understanding the martingale property

Showing the Itô logarithm is the inverse of the Doléans-Dade exponential

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