Question

Optimal strategies in a simple game when facing gambler's ruin

score 167 · Answer 1 · 2026-03-25 17:39:23

167

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Optimal strategies in a simple game when facing gambler's ruin

Published on 25 Mar 2026 - 17:39

score 86 · Answer 2 · 2020-04-18 15:38:58

86

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How to show $\mathbb E U_{\nu^}=\mathbb E U_0 \implies \forall n \in \mathbb N: \mathbb E U_{\nu^ \wedge n}=\mathbb E U_0$ in Snell envelope?

Published on 18 Apr 2020 - 15:38

score 246 · Answer 3 · 2020-04-18 17:27:42

246

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Random variable measurable with respect to stopped sigma algebra

Published on 18 Apr 2020 - 17:27

score 73 · Answer 4 · 2020-04-18 23:20:28

73

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$\mathbb{E}[\xi|\mathscr{F}_{\sigma}] = \mathbb{E}[\xi|\mathscr{F}_{\sigma \wedge \tau}] $ on $\{ \sigma \le \tau\}$

Published on 18 Apr 2020 - 23:20

score 35 · Answer 5 · 2020-04-20 13:46:24

35

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If $\hat{t}$ is a stopping time, provide an example illustrating how $(\hat{t}-1)\wedge 0$ is indeed not a stopping time

Published on 20 Apr 2020 - 13:46

score 96 · Answer 6 · 2020-04-20 15:43:48

96

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If $G$ is a sub-filtration on $F$ (i.e.$G_t \subset F_t$), then prove that for a stopping time $\tau$ that $G_\tau \subset F_\tau$

Published on 20 Apr 2020 - 15:43

score 583 · Answer 7 · 2020-04-21 20:32:23

583

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Does Wald's equation hold when the expected stopping time is infinite?

Published on 21 Apr 2020 - 20:32

score 554 · Answer 8 · 2020-04-23 14:19:56

554

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Can a super-martingale with stopping time end with infinite value in expectation?

Published on 23 Apr 2020 - 14:19

score 307 · Answer 9 · 2026-03-26 10:39:57

307

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Planar Brownian Motion hitting times

Published on 26 Mar 2026 - 10:39

score 461 · Answer 10 · 2020-04-26 22:57:59

461

Views

Proof of Optional Stopping Theorem

Published on 26 Apr 2020 - 22:57

score 910 · Answer 11 · 2020-04-28 21:04:29

910

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Use the martingale $M_t = \exp(\theta B_t − \theta^2t/2)$, $\theta \in \mathbb{R}$, to find $P(\tau_a < \tau_b)$

Published on 28 Apr 2020 - 21:04

score 357 · Answer 12 · 2020-04-29 22:43:19

357

Views

Exponential bound for tail of exit time from [-b,b] of martingale

Published on 29 Apr 2020 - 22:43

score 31 · Answer 13 · 2020-05-02 21:42:44

31

Views

$\bigcap_{t>T}\{|B_t| >0\}$ is not $\mathcal{F}_T$ measurable.

Published on 02 May 2020 - 21:42

score 186 · Answer 14 · 2020-05-03 09:34:42

186

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Is jump time in a continuous-time Markov chain a stopping time?

Published on 03 May 2020 - 9:34

score 156 · Answer 15 · 2020-05-03 17:55:20

156

Views

Lower bounding the probability that a submartingale passes a threshold

Published on 03 May 2020 - 17:55

List Question

Optimal strategies in a simple game when facing gambler's ruin

How to show $\mathbb E U_{\nu^}=\mathbb E U_0 \implies \forall n \in \mathbb N: \mathbb E U_{\nu^ \wedge n}=\mathbb E U_0$ in Snell envelope?

Random variable measurable with respect to stopped sigma algebra

$\mathbb{E}[\xi|\mathscr{F}_{\sigma}] = \mathbb{E}[\xi|\mathscr{F}_{\sigma \wedge \tau}] $ on $\{ \sigma \le \tau\}$

If $\hat{t}$ is a stopping time, provide an example illustrating how $(\hat{t}-1)\wedge 0$ is indeed not a stopping time

If $G$ is a sub-filtration on $F$ (i.e.$G_t \subset F_t$), then prove that for a stopping time $\tau$ that $G_\tau \subset F_\tau$

Does Wald's equation hold when the expected stopping time is infinite?

Can a super-martingale with stopping time end with infinite value in expectation?

Planar Brownian Motion hitting times

Proof of Optional Stopping Theorem

Use the martingale $M_t = \exp(\theta B_t − \theta^2t/2)$, $\theta \in \mathbb{R}$, to find $P(\tau_a < \tau_b)$

Exponential bound for tail of exit time from [-b,b] of martingale

$\bigcap_{t>T}\{|B_t| >0\}$ is not $\mathcal{F}_T$ measurable.

Is jump time in a continuous-time Markov chain a stopping time?

Lower bounding the probability that a submartingale passes a threshold

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