List questions from stochastic-calculus

Published on 26 Mar 2026 - 3:00

166

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The real and imaginary parts of $X_t = \exp[iuN_t - \lambda t(e^{iu}-1)]; \; 0 \le t < \infty$ are martingales

Published on 30 Mar 2026 - 15:08

199

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Problem 1.3.24 (ii) Karatzas and Shreve $E[X_{T \wedge t}|\mathscr{F}_S]\ge X_{S \wedge t}$ for $S \le T$ and submartingale $X$.

Published on 30 Mar 2026 - 15:05

201

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Karatzas and Shreve Problem 1.3.24(i). $X_{T \wedge t}, \mathscr{F}_t$ is a submartingale.

Published on 30 Mar 2026 - 15:08

44

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Determine all the -measurable real-valued random variables on $Ω$.

Published on 04 Dec 2019 - 4:35

240

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Show that a SDE has no solution

Published on 26 Mar 2026 - 2:53

1.4k

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Using Ito Isometry to find the mean and variance of an Ito Stochastic Integral

Published on 27 Mar 2026 - 22:12

139

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$n$-th power of stochastic exponential

Published on 27 Mar 2026 - 22:11

150

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Karatzas and Shreve proof : An increasing random sequence $A$ is predictable if it is natural

Published on 30 Mar 2026 - 16:45

117

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Possibility that there is a week where everyday someone has birthday (among 250 people)

Published on 05 Dec 2019 - 12:46

650

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Quadratic variation of the compensated Poisson process $N_t - \lambda t$

Published on 27 Mar 2026 - 0:02

158

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Karatzas and Shreve use of the localization technique to prove convergence in probability of the quadratic sum of $X$ to $\langle X \rangle_t$.

Published on 05 Dec 2019 - 20:59

1.3k

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Prove that portfolio is self financing?

Published on 26 Mar 2026 - 2:54

102

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What to use as numeraire in pricing the derivative?

Published on 28 Mar 2026 - 5:22

55

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For BM $W$ starting at $x \in [0,a]$, the probability that $W$ hits $0$ before $a$

Published on 07 Dec 2019 - 10:49

List Question

Comparison theorem for the following linear SDE

The real and imaginary parts of $X_t = \exp[iuN_t - \lambda t(e^{iu}-1)]; \; 0 \le t < \infty$ are martingales

Problem 1.3.24 (ii) Karatzas and Shreve $E[X_{T \wedge t}|\mathscr{F}_S]\ge X_{S \wedge t}$ for $S \le T$ and submartingale $X$.

Karatzas and Shreve Problem 1.3.24(i). $X_{T \wedge t}, \mathscr{F}_t$ is a submartingale.

Determine all the -measurable real-valued random variables on $Ω$.

Show that a SDE has no solution

Using Ito Isometry to find the mean and variance of an Ito Stochastic Integral

$n$-th power of stochastic exponential

Karatzas and Shreve proof : An increasing random sequence $A$ is predictable if it is natural

Possibility that there is a week where everyday someone has birthday (among 250 people)

Quadratic variation of the compensated Poisson process $N_t - \lambda t$

Karatzas and Shreve use of the localization technique to prove convergence in probability of the quadratic sum of $X$ to $\langle X \rangle_t$.

Prove that portfolio is self financing?

What to use as numeraire in pricing the derivative?

For BM $W$ starting at $x \in [0,a]$, the probability that $W$ hits $0$ before $a$

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