Taylor Martin

University of California Los Angeles, CA

mathtm.blogspot.com

I am a recent graduate in applied mathematics at UCLA and currently trying to break into the quantitative investment/trading industry while also continuing to pursue advanced graduate-level mathematics as both a hobby and career necessity.

Jan
17
revised Deriving the definition of stochastic integrals with respect to Ito processes from first principles
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Jan
17
comment Deriving the definition of stochastic integrals with respect to Ito processes from first principles
@TheBridge - Regarding your second comment, the convergence is true for each $t\geq0$ in $L^{p}(\Omega)$ ($1\leq p\leq2$) no matter how you construct the sequence of partitions $\Pi_{n}$ as long as $||\Pi_{n}||\to0$. As is well known, you can construct a particular sequence $\Pi_{n}$ so that for a fixed $\omega$, $\text{QV}^{2}(W)(\omega)=\alpha$ for any $\alpha>0$ including $+\infty.$ However, you can avoid all of this by demanding that $||\Pi_{n}||\to0$ such that $\sum_{n=1}^{\infty}||\Pi||_{n}<\infty$; then by Borel-Cantelli the QV process does converge pathwise $\omega$-a.s. to $t$.
Jan
17
comment Deriving the definition of stochastic integrals with respect to Ito processes from first principles
@TheBridge - Regarding your first comment, please provide your definition if you disagree with mine; however, I am using the definition that is regularly encountered in mathematical finance texts. Also, there really isn't any need to be pedantic here with the conditions of the coefficient processes; they are more or less implied and in any case you can just assume the ones regularly imposed: adadpability, $L^{2}(\Omega\times[0,t])$ integrable, and $\omega$-a.s. continuous as a function of $t$.
Jan
15
revised Deriving the definition of stochastic integrals with respect to Ito processes from first principles
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Jan
15
revised Deriving the definition of stochastic integrals with respect to Ito processes from first principles
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Jan
15
revised Deriving the definition of stochastic integrals with respect to Ito processes from first principles
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revised Deriving the definition of stochastic integrals with respect to Ito processes from first principles
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Jan
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revised Deriving the definition of stochastic integrals with respect to Ito processes from first principles
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revised Deriving the definition of stochastic integrals with respect to Ito processes from first principles
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Jan
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asked Deriving the definition of stochastic integrals with respect to Ito processes from first principles
Jan
15
revised Deriving the definition of stochastic integrals with respect to Ito processes from first principles
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Jan
15
revised Deriving the definition of stochastic integrals with respect to Ito processes from first principles
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Jan
15
revised Deriving the definition of stochastic integrals with respect to Ito processes from first principles
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Jan
15
revised Deriving the definition of stochastic integrals with respect to Ito processes from first principles
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Jan
15
revised Deriving the definition of stochastic integrals with respect to Ito processes from first principles
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Jan
15
revised Deriving the definition of stochastic integrals with respect to Ito processes from first principles
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Jan
15
asked Deriving the definition of stochastic integrals with respect to Ito processes from first principles
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Jan
8
comment Octave/Matlab - Optimizing CSV Import - Speeding Up datenum
Okay - so I've devised a method to get the first line at which m = dBegin is found and the last line on which n = dEnd is found. How do I tell textscan to read this range? I could of course put N := m - n, but I'm not sure how to set the file pointer at line m.
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