# Tagged Questions

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### Locate proof of Second Fundamental Theorem of Asset Pricing

Where can I find a $\textbf{rigorous}$ proof of the Second Fundamental Theorem of Asset Pricing. That is, A market is complete if and only if it has a unique risk neutral measure. Please do not ...
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### Multi-dimensional Feynman Kac Theorem

I am trying to understand how to prove the multi-dimensional version of the Feynman-Kac formula. The single-dimensional version is proved on this page: en.wikipedia.org/wiki/Feynman–Kac_formula ...
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### Stationary distribution for OU process driven by fractional brownian motion

Consider the SDE driven by a fractional brownian motion $$dX_t = \kappa (\omega - X_t) dt + \eta dW_t^{H}$$ where $W_t^{H}$ is a fractional brownian motion with Hurst parameter H. I am interested ...
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### Resource for Stochastic Calculus and Ito processes

May someone please recommend a book or website where one can learn Stochastic Calculus and Ito processes from scratch.
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### Weak stochastic integral

I recently encountered the following object, referred to as "weak stochastic integral" in the book of SPDE's by Prévôt/Röckner [PR07]: $$\int_0^T \langle \Psi \,\mathrm dW(t), \Phi(t)\rangle$$ A ...
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### optimization problem in mathmetical finance using convex duality

I'm interested in the application of stochastic processes and stochastic calculus in mathematical finance. In my lecture I often see a certain optimization problem usually of a convex function. ...
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### New stochastic calculus

I am interested in Kagi and Renko approach and hope I can use it for a random walk process. I searched for it on internet but I couldnt find any basic material to read about it. Can someone please ...
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### Stochastic processes with non-zero higher order variations

I'm under the impression that how non-zero quadratic variation of the Brownian motion results in Itō's lemma or in general, the creation of the Itō's calculus. I'm also aware that stochastic integral ...
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### Good books on “advanced” stochastic analysis

Any good books suggestion for studding advanced features of stochastic analysis ? Thank's in advance
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### general semimartingale theory

Last semester I attended a course about stochastic calculus. There we constructed the stochastic integral with respect to continuous semimartingales. We restrict ourselves to the continuous case. ...
### Solving SDE's on subsets of $R^n$.
It is well-known (see for instance Oskendal's text) that if $T>0$ and b(\cdot,\cdot): [0,T] \times \mathbb{R}^n \rightarrow \mathbb{R}^n~~~~~~\sigma(\cdot,\cdot):[0,T] \times \mathbb{R}^n ...