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Questions tagged [radon-nikodym]

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Let $\mathbb{P} \sim \mathbb{Q} \sim \mathbb{R}$ be equivalent probability measures on some measurable space

Let $\mathbb{P} \sim \mathbb{Q} \sim \mathbb{R}$ be equivalent probability measures on some measurable space $(\Omega, \mathcal{F})$, and let $\mathcal{G} \subset \mathcal{F}$ be a sub- $\sigma$-...
codelearner's user avatar
3 votes
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Understanding the asset pricing theory and numeraire

While reading about asset pricing theory and numeraire, I had faced some confusion. Short summary of asset pricing theory from my book We start our journey with a risky asset $S_t=\mu S_tdt+\sigma ...
emonhossain's user avatar
2 votes
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200 views

Are Stochastic Differential Equation diffusion terms always invariant under a change of measure?

I'm struggling with learning change of numeraire, and stochastic differential equations. I'm reading the beginning of Brigo and Mercurio's Interest Rate Models- Theory and Practice, and I'm on the ...
Alex Lapanowski's user avatar
2 votes
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249 views

Understanding Bayes Rule of conditional expectation

Let $\mathcal{F}$ be a $\sigma$-algebra, $P$ and $Q$ be equivalent martingale measures and $\frac{dQ}{dP}$ the Radon Nikodym Derivative. I learned that $\Bbb{E}_Q[X]=\Bbb{E}_P[\frac{dQ}{dP}X] $, which ...
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1 vote
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Equivalence of formulations of Radon Nikodym derivative

Let $N$ be a numeraire associated with the probability measure $Q^N$ and $U$ be a numeraire associated with the probability measure $Q^U$, both of which are equivalent to the physical probability ...
NC520's user avatar
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The Radon-Nikodym derivative for a sequence of dependent variables

Suppose that a probability space $(\Omega, \Sigma, \mathbb{P})$ is given. Let $W=\{W_n\}_{n\in \mathbb{N}_0}$ be a sequence of $\mathbb{P}$-i.i.d real-valued random variables on $\Omega$. Furthermore, ...
user53249's user avatar
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Association between a random variable and Radon-Nikodym derivative

Suppose that $X$ is a random variable and $\frac{d\mathbb{Q}}{d\mathbb{P}}$ is the Radon-Nikodym derivative. The quantity under consideration is as follows: \begin{equation} Cov(X, \frac{d\mathbb{Q}}{...
user53249's user avatar
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Change of numeraire between t1-forward mesure and t2-forward mesure

Let denote $\mathbb{Q}_{t_1}$ the $t_1$-forward mesure associated to zero coupon bond $B(.,t_1)$. Let denote $\mathbb{Q}_{t_2}$ the $t_2$-forward mesure associated to zero coupon bond $B(.,t_2)$. I am ...
DeepInTheQF's user avatar
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2 answers
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Understanding the Impact of Illiquidity on Equivalent Martingale Measures (EMMs) in a Simple Market

I'm currently studying a simple market model with an asset $S$ whose price follows a geometric Brownian motion ($dS_t=S_t(μdt+σdW_t)$) and a risk-free asset $B$ ($dB_t=B_trdt$) over a finite horizon $...
ActuaireDeStrasbourg's user avatar