# Questions tagged [equivalent-measure]

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### Why the Esscher transform is the right transform for pricing formula?

A Wiener process has infinitely many states of the world at any time step. Does that not mean that there are infinitely many EMM's for any model that uses the Wiener process? But then if there is only ...
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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- $\sigma$-...
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### Equivalent local martingale measure vs. equvalent martingale measure in a Brownian setup

Assume you have the standard financial market built up of a Brownian motion. I have seen some books say that an equivalent local martingale measure imples no arbitrage, and some say that an equivalent ...
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### Poisson process under equivalent martingale measure

I have a stochastic process $N(t)$ which is equal to $n$ with probability $P\{N(t) = n\}=\frac{\left(\lambda t \right)^{n}}{n!}e^{-\lambda t }$ where $t$ represents the time period. In other words, ...
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### Is first order stochastic dominance conserved under change of measure?

As the title states, my question is whether first order stochastic dominance is conserved under change of measure, for instance from the $\mathbb{P}$ measure to $\mathbb{Q}$ measure and change of ...
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### How to prove that the following is still a Brownian motion [closed]

Given a Brownian motion $B_t$ on a filtered probability space, how can I prove that $W_t=B_t+\alpha t$ is still a Brownian motion, with $\alpha \in \mathbb{R}$? Is it always true? Do I need necessarly ...
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### Is $E_t^{Q}(g(Y))=E_t^{Q^Z}(g(Y))$?

Consider $$Z(t)=\left(\frac{S(t)}{H}\right)^p$$where $S$ has a standard Black-scholes Dynamics for a stock, $H$ is a postive constant and $p =1 - \frac{2r}{\sigma^2}$ and a simple claim with a pay-off ...
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### Market Price of Risk for Consumption Asset - Hull's Example 28.1

In Hull's Options, Futures, and Other Derivatives, he gives an example 28.1 as below. Consider a derivative whose price is positively related to the price of oil and depends on no other ...
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