Question

Show that $\mathbb{E}\left[c_{\tau\wedge n}X_{\tau\wedge n}-\sum_{i=1}^{\tau\wedge n}c_i\mathbb{E}(X_i-X_{i-1}\mid\mathcal{F}_{i-1})\right]\le 0$

score 94 · Answer 1 · 2015-08-09 01:07:03

94

Views

Show that $\mathbb{E}\left[c_{\tau\wedge n}X_{\tau\wedge n}-\sum_{i=1}^{\tau\wedge n}c_i\mathbb{E}(X_i-X_{i-1}\mid\mathcal{F}_{i-1})\right]\le 0$

Published on 09 Aug 2015 - 1:07

score 159 · Answer 2 · 2026-03-29 07:34:42

159

Views

Independence of a hitting time and the underlying stochastic process

Published on 29 Mar 2026 - 7:34

score 161 · Answer 3 · 2015-08-15 17:45:08

161

Views

Stochastic variables independent given Tau

Published on 15 Aug 2015 - 17:45

score 94 · Answer 4 · 2015-08-24 15:19:50

94

Views

Does this game make you arbitrarily rich with probability one?

Published on 24 Aug 2015 - 15:19

score 161 · Answer 5 · 2015-08-31 23:11:11

161

Views

On the proof of lemma 1.2.4 of Stroock and Varadhan A question concerning stopping times

Published on 31 Aug 2015 - 23:11

score 256 · Answer 6 · 2015-09-16 02:39:30

256

Views

Stopping time proof with discrete martingale

Published on 16 Sep 2015 - 2:39

score 682 · Answer 7 · 2015-09-18 10:40:49

682

Views

A martingale characterization

Published on 18 Sep 2015 - 10:40

score 214 · Answer 8 · 2015-09-18 19:30:34

214

Views

Exist $\alpha < \infty$, $\beta > 0$ such that $\mathbb{P}\{T_\lambda > t\} \le \alpha e^{-\beta t}?$

Published on 18 Sep 2015 - 19:30

score 490 · Answer 9 · 2015-09-22 21:17:37

490

Views

Why do we need optional stopping theorem?

Published on 22 Sep 2015 - 21:17

score 91 · Answer 10 · 2015-09-26 15:44:47

91

Views

Is there any intuition behind the statement $E[X_\tau \mid \mathcal{F}_\sigma]=X_\sigma$

Published on 26 Sep 2015 - 15:44

score 822 · Answer 11 · 2015-09-28 13:48:21

822

Views

If $X$ is an $\mathcal F_t$-adapted process with countable time domain and $\tau$ is a stopping time, then $X_\tau$ is $\mathcal F_\tau$-measurable

Published on 28 Sep 2015 - 13:48

score 243 · Answer 12 · 2015-09-29 12:13:24

243

Views

If $(F_t)_t$ is a filtration, $T$ is a stopping time and $Y$ is $F_T$-measurable, then $1_{\left\{T=s\right\}}Y$ is $F_s$-measurable

Published on 29 Sep 2015 - 12:13

score 3.4k · Answer 13 · 2015-10-06 14:33:47

3.4k

Views

Showing stopping is finite almost surely

Published on 06 Oct 2015 - 14:33

score 508 · Answer 14 · 2015-10-08 13:46:23

508

Views

Prove $\tau=\inf\{t\in[0,T]:M_t=0\}\wedge T$ a stopping time for a continuous martingale $(M_t)_{t \geq 0}$

Published on 08 Oct 2015 - 13:46

score 445 · Answer 15 · 2015-10-11 17:48:59

445

Views

Show submartingale property.

Published on 11 Oct 2015 - 17:48

List Question

Show that $\mathbb{E}\left[c_{\tau\wedge n}X_{\tau\wedge n}-\sum_{i=1}^{\tau\wedge n}c_i\mathbb{E}(X_i-X_{i-1}\mid\mathcal{F}_{i-1})\right]\le 0$

Independence of a hitting time and the underlying stochastic process

Stochastic variables independent given Tau

Does this game make you arbitrarily rich with probability one?

On the proof of lemma 1.2.4 of Stroock and Varadhan A question concerning stopping times

Stopping time proof with discrete martingale

A martingale characterization

Exist $\alpha < \infty$, $\beta > 0$ such that $\mathbb{P}\{T_\lambda > t\} \le \alpha e^{-\beta t}?$

Why do we need optional stopping theorem?

Is there any intuition behind the statement $E[X_\tau \mid \mathcal{F}_\sigma]=X_\sigma$

If $X$ is an $\mathcal F_t$-adapted process with countable time domain and $\tau$ is a stopping time, then $X_\tau$ is $\mathcal F_\tau$-measurable

If $(F_t)_t$ is a filtration, $T$ is a stopping time and $Y$ is $F_T$-measurable, then $1_{\left\{T=s\right\}}Y$ is $F_s$-measurable

Showing stopping is finite almost surely

Prove $\tau=\inf\{t\in[0,T]:M_t=0\}\wedge T$ a stopping time for a continuous martingale $(M_t)_{t \geq 0}$

Show submartingale property.

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