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Art markets typically have huge transaction costs of the order of 10%, caused by buyers premium and auction fees. Therefore long holding periods are unavoidable, with long-term returns somewhere between those of bonds and equities. By its very nature, art is not easily replicated so arbitrage or derivatives are out. The rationality of agents (aka collectors) ...

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For Q1, the function $a(t)$ is the instantaneous correlation. The form given by (2) is basically the Cholesky decomposition. Of course, you may directly show, uisng Levy's characterization, that $$\widetilde{W}(t) = \int_0^t\bigg[\frac{1}{\sqrt{1-||a(t)||^2}} dZ(t) -\frac{a(t)^T}{\sqrt{1-||a(t)||^2}} dW^B(t) \bigg]$$ is a standard scalar Brownian motion ...

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Q1: $$(1)\rightarrow(2)$$ (1): $a(t)$ is the instantaneous correlation of $\rho(Z_t,W_t)$ because: $$\rho(dZ_t,dW_t)=\dfrac{Cov(dZ_t,dW_t)}{\sigma_{dZ_t}\sigma_{dW_t}}=\dfrac{E(dZ_t\cdot dW_t)}{\sqrt{dt} \sqrt{dt}}=\dfrac{\langle dZ_t, dW_t\rangle}{t}=a(t)$$ $\Rightarrow$ (2) holds as following, in the 1-dim case: $dZ_t\sim N(0,dt),$ ...

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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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I would say the financial- and the art market is very different, only the roots of the market / auctions is the same. As the art market is unique and very illiquid, alot of the strategies from the modern financial market simply does not apply. I have been building (and still maintains) a toolbox of models, which mostly try to find trends based on multiple ...

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EDIT: I changed the answer to have it more on topic. Summary It boils down to Mark Joshi's answer. I wanted to add something more. Answer A probability measure $Q1$ and a numeraire $N1(t)$ are associated if all prices expressed relative to $N1$ are martingales under $Q1$: \frac{price(t)}{N1(t)} = \mathbb{E}^{Q1} \left[ \left. \frac{price(T)}{N1(T)} \, ...

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