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A function $f : \mathbb R^n\backslash\{0\} →\mathbb R$ is called (positive) homogeneous of degree $k$ if $$f(\lambda \mathbf x) = \lambda^k f(\mathbf x) \,$$ for all $\lambda > 0$. Here $k$ can be any complex number. The homogeneous functions are characterized by Euler's Homogeneous Function Theorem. Suppose that the function $f : \mathbb R^n ... 9 At the top of this list I still recommend you to seek employment in order to learn from others in QF space. Could you possible work in a quant team within an investment bank where you currently reside? Start to reach out to the quant finance community so you are connected once you decide to locate to where you can practice this discipline.reach out to ... 8 Edit: Freddy's answer is good -- we wrote concurrently. He rightly points out that QF is a broad field, and that it is among other things a community. Here, I describe a practical, down-to-earth path for getting your feet wet in one key piece of it -- software and model development for derivatives analysis, starting with vanilla options. Your best bet ... 4 You see, you added something new to the source formula, i.e. a dependence between weights of different assets:$w_2 = 1 - w_1$. Let's try to forget that they are related to each other and vary them independently: $$\sigma(x)=\sqrt{w_1^2 \sigma_1^2 + w_2^2 \sigma_2^2 + 2 w_1 w_2 \sigma_{1,2}}$$ Now$\frac{dw_2}{dw_1} = 0$and equation becomes: $$\frac{d ... 4 The other answers are useful and sensible. I have worked full time in equity research for nearly two decades, so very much a "qualitative" rather than a quantitative approach. However, all the firms for which I have worked had quants and because of my casual interest in the area I've spent a lot of time talking to quant teams over the years, often over a ... 3 I think one of the best (and very current) articles about how to break into QF (for any kind of background) is: "On becoming a Quant" by Mark Joshi For your special background in mathematics see this excerpt from section 9: The main challenge for a pure mathematician is to be able to get one’s hands dirty and learning to be more focussed on getting ... 3 The general idea is to bootstrap the discount factors in the correct order, based on the data you have given. I'm going to make some assumptions that your bonds are paying annual coupons. The longest maturity is 2.5 years, meaning you need discount factors for 6M, 1.5Y and 2.5Y. The 6M deposit has a rate of 5%, this tells you that you should use the 5% rate ... 2 The essence of discounting is that now is less risky than later. So a contract to deliver £1 in 1 year is more risky than one to deliver £1 tomorrow, (the counterparty could suffer a credit event) so it is worth less. Discount factors multiply; if I know that £1 at 1y is worth £0.98 today, and £1 at 2y is worth £0.98 at 1y (i.e. equal rates for both ... 2 The state price vector are the prices of securities which pay \1 if and only if that state of the world occurs. This is just a question of being able to replicate the payoffs$$ \begin{pmatrix} 1 \\ 0 \\ 0 \end{pmatrix}, \begin{pmatrix} 0 \\ 1 \\ 0 \end{pmatrix}, \begin{pmatrix} 0 \\ 0 \\ 1 \end{pmatrix}$$with payoff vectors$\vec{b} = [1,1,1]^T\$ and ...

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Although I don't think that this is a question that fits in here, I will give you a reference. You might want to have a look at the so called greeks, you find a first overview here: http://en.wikipedia.org/wiki/Greeks_(finance)

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Riemann Hypothesis is a very import conjecture in mathematics, but it also an extremely hard problem, top mathematicians have worked on it for over 100 years and could not solve it. Moreover, one cannot start to really think about it without proper understanding of the problem; it might take years to understand what is going on even for people with strong ...

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