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Orthogonality and independence are different concepts. The concepts are the same for Wiener processes because in the context of normal random variables, independence is equivalent to orthogonality (i.e. uncorrelatedness) Independence is the standard definition for probability. Let $\mathcal{F}, \mathcal{G}$ be the sigma algebras generated by two ...


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I have asked myself the very same question when I first read the book. As far as I can tell, the "scalability" condition is only imposed for technical reasons. It simplifies the subsequent proof of the Fundemental Theorem of Asset Pricing in constrained markets. There are several papers that have shown that the theorem is valid for conic constraints. ...


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A very good book covering such fundamentals with no or only a minimal amount of maths — highly recommended! Puzzles of Finance: Six Practical Problems and Their Remarkable Solutions by Mark P. Kritzman The topics that are covered here are: Siegel's Paradox Likelihood of Loss Time Diversification Why the Expected Return Is Not To Be Expected Half Stocks ...


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There is a very famous math finance cheat sheet already (by Prof. Wystup), you can find the content here: https://mathfinance2.com/Products/CheatSheet#Content


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At this stage your sheet is focus on "stochastic calculus for derivative pricing". It is just a subset of math finance. You are missing: risk management (VaR, quantiles, etc) -- more statistics than stochastic calculus. See for instance the content of Attilio Meucci's book. quantitative trading (optimal trade scheduling, smart order routing, ...


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Sure, the variance of the total wealth can be expressed in terms of the variances and covariances of the prices of the assets. If $$ W = \sum_{i} \pi_i P_i $$ where $\pi_i$ is the total dollar amount invested in asset $i$ with price $P_i$. The variance of total wealth is then $$ Var(W) = \sum_i \pi_i Var(P_i) + \sum_i \sum_{j, j\neq i} \pi_i \pi_j Cov(P_i, ...



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